It can happen when the bearing is so tight that it damages the post when removed. Unscrewing a yoyo will remove the bearing from one of the sides so it’s possible to happen like that. If one side is looser than the other it will come off that side when you unscrew and not cause an issue unless you use a tool to force it off the other side.
You can’t really screw it back together other than cross threading or having something stuck under the bearing.
How likely is it that an axle can become distorted in the axle hole / threads, e.g. the axle screw goes in “loose”? 
As long as it’s not cross threaded, there shouldn’t be any issues.
I was going to say this too. Some throws with floating axles have this issue - although I personally find this sort of vibe negligible.
By “floating axle” I mean when an axle does not thread completely into both halves of the yoyo. So the axle can sit further into the “left” or “right” half of the yoyo rather than being completely center. Although, I’ve also heard the argument that floating axles actually reduce vibe when centered in the yoyo because they don’t sit flush against the inside walls. Who knows. I just throw things. 
I definitely have “messed up” a yo-yo by unscrewing it.
That said, I’m not sure if it was the unscrewing that caused the problem or if perhaps it just revealed a problem.
What I mean is like I wonder if impacts can have an effect on the axle, but as long as the yo-yo stays screwed tight as it is, it will play OK. Then, when you take it apart, the bend or twist or flaw or weak point of whatever is wrong with the axle reveals itself and when you screw it back in it becomes wonky.
For that reason alone I don’t take it apart unless it is absolutely necessary which basically is only to change the bearing or the pads.
If you think about what is happening when you screw a yo-yo together, you’re pressing the bearing seats against the bearing.
So as long as …
… even if the axle hole was not perfectly straight, or the threads or loose, the yo-yo will want to become flush and flat against each of the sides as you tighten it. So I think flush / flatness isn’t a problem, unless the bearing seats or the bearing are really messed up?
I’m not entirely sure what happens – in the case of a loose bearing seat – when the bearing isn’t quite perfectly “centered” as you tighten it though.
In that case the bearing is not in the absolute “correct” center of the yo-yo. That’s about the only variable I can think of when it comes to unscrewing and re-screwing a yo-yo?
I don’t believe that is as true as you may think. I’d guess (it’s only a guess) that if they assemble a yo-yo and it has noticeable vibe they will try a different half. I bet most that they assemble are just left assembled. I don’t think there’s a bunch of trial and error assembling halves and mixing and matching to find the “best tuned” combinations. The logistics of that seem pretty extensive and very time consuming.
And as far as the OP, I don’t think there’s a problem taking your yoyo apart if you use some mild due care when putting it back together.
I am who OP is referencing. @codinghorror , I appreciate you opening up this topic. My yoyo was 10/10 smooth like butter, and now had an 8/10 vibe on grinds after one unscrew. I love my tiwalker and I do not mean to say that this is a major bummer or anything, just something that happens. 
It really does not disappoint me at this point but I love the nitty gritty tuning stuff and have always had a knack for making my yoyos as smooth as can be, so I contacted OP about the issue I had.
This is my opinion and I would love to be enlightened on the subject if what I am saying is totally incorrect. I have been yoyoing for 10 years and am careful when unscrewing my throws. Never stripped a yoyo before. Usually use a string pick so I dont have to unscrew.
My theory as to how some yoyos get vibe when they are unscrewed focuses on the bearing seat tightness. I feel as if when you get a yoyo with a tight bearing post and a bearing with a tight inner race, it can induce vibe after taking apart the yoyo once due to galling of the bearing post while unscrewing. When the bearing seat becomes more loose and uneven, it creates the potential for a disconnect between the bearing post and the inner race of the bearing.
I find this happens on yoyofactory throws to me frequently, newer ones in particular. The bearing post and bearing are tight, and when you unscrew it you can see much of the anodizing on the bearing post will come off and your yoyo will have some vibe.
In particular, one drop yoyos never do this to me. They are always smooth and stay smooth after unscrewing, though the bearings seem to sit loosley around the post relative to other brands.
I unscrewed my Replay pro twice. Can’t get it to not wobble like a penguin now. After the first time it was jacked. Unscrewed it again, examined threads, can’t find an issue. Screwed it back together and it’s slightly better but still not dead smooth as it arrived. I haven’t unscrewed anything metal since.
The Big Fun is supposedly “tune-able” there’s even a video by BJ, I must have some sort of filter on my machine because I don’t see where the tuning is happening and my Big F💩n plays like garbage also.
Up until the Replay Pro issue I must have unscrewed 300 throws and never had an issue but the experience has made me skittish so I don’t take chances any longer.
I think plastics have a legitimate concern here that metals do not.
For one thing, the metal part around the bearing and wells WILL defeat the plastic, quite easily, if you tighten it too much. That’s far more likely than on an aluminum yoyo!
This is why plastics often have those little arrow marks on the rims to show you where to tighten to.
I am surprised the discussion is more about bearing tightness as opposed to location of axle. From experience, the changes that have the highest likelihood to affect vibe for me is with messing with the axle, and how tight you screw the halves in. As for bearing, any decent bearing is basically perfectly round, and as long as you can’t feel it moving on the bearing seat when you push it around, really all you can do is flip it. I think people miss that as far as tuning induced vibs are concerned, most of the time isn’t about something being off centered, but off axis, ie the halves are off set not by a shift but a tilt.
If the yoyo is well made, it would be vibeless regardless where the axle and how tight you screw in the halves. But a yoyo that have a slight offset or tilt may have a axle configuration that eliminates the offset and tilt. This is why i keep a bunch of axle, sometimes a vibey yoyo can have alot of the vibe tuned out with a slightly bent axle. It has a lot less to do with how tight the bearing seat is, and more to do with how well the axle hole is drilled.
Edit: I wonder whether there is a way to intentionally put in a tilt in such a way that makes a yoyo more tunable. If you are gunning for a dead center yoyo, its great and all that you can always unscrew and rescrew, but once you ding it a few times, it also locks you in with the vibe. But I got a yoyo that is very sensitive to axle location, and I have since dinged the crap out of it, but so far I have been able to tune the vibe out very well, given that I have to use a shorter axle so I got more room to “play”.
I’ve been doing this yoyo thing before yoyos came apart. And never had a problem with vibe after unscrewing a yoyo. But since I dont worry about subtle vibe maybe it’s there and I dont care to notice it - A revelation.
Yes, after messing so much with tuning, the lesson learnt is i would be a much better yoyoer if i spent that time just throwing the yoyo. You cant tune a vibey yoyo to G2 smooth, and you cant tune a pulse vibe yoyo to have no pulse vibe.
This actually makes a lot of sense and would explain why even people who are careful when screwing/unscrewing yoyos still have potential issues. This could also be what the OD guys refer to as “damaging the bearing seat”; that along with literally damaging it when wiggling the bearing out with a removal tool.
Personally, I like many others only take apart the yoyo if it is absolutely necessary. I treat it as a ritual and try my best to be as smooth as possible (I live on a farm, so im used to nuts and bolts and the like). So far I have never had any issues, but I have had quite a few yoyos where the ano would come off when removing the bearing. I have always believed that unscrewing a yoyo would not damage it in any way, but the above point makes me just a little unsure. Perhaps it would be most wise to add some lube to the bearing seat to minimize that possibility?
The only times I had this happen were with old anti yos. The axles in them werent long enough and they sometimes needed “tuning”. I remember the the oxy designs had a sweet spot as well as they didnt have a fixed gap. 99% = several hundred yoyos had no issue I could tell.
I also have to admit that I dont spend a lot of time holding my fingernail against a yoyo.
This does not seem to be well understood, or even accepted. There is no question that the phenomenon is real. I put my money on floating axles moving around over bearing seat damage. Ive got some old CLYW that are deeply marred around the bearing seat from a decade of use and unscrewing. Ano no where to be found, and still glass smooth. But any throws I have with really short axles are more prone to this.
TBH, my TiVayder did the same thing after first disassembly (very minor), but Ive been able to re-tune it back to smooth again. Have not ran into that again after many many more unscrews. Not a problem.
If your axle is short, and does not have hex hole to tighten them up (Looking at you YYR) than these will be the most prone to floating and may induce minor vibe depending on where the axle lands inside the threads. But isn’t limited to only short axles throws.
Guess im on team Axle, and not team Bearing Seat.
Does anyone else remember the old “Tuning” Guide booklet? I just came across mine last week. Back in the Renegade/FH days someone wrote a manual on how to tune a yoyo. Seems these days that’s a lost art.
Should write up a “How to tune a modern yoyo” manual.
On a spinning object it can be one of a number of things: axle, bearing seat, bearing, etc.
I found these for tuning
I did notice that the first unscrew is very tight with the Vayder, and likely tighter with more / thicker anodization on grey and black. That tends to be true on all yo-yos.
This doesn’t make sense to me because once fully tightened the metal sides of the bearing well are perfectly flat and flush against the bearing, the axle makes zero difference. But if the sides of the bearing or the yo-yo aren’t perfectly flat…
The thought is that if the axle isn’t centered between the halves that can induce vibe. Some older Difs and AntiYos had short axles. People would use a couple different methods to center the axle. I honestly don’t know if the non centered axle would induce vibe or not. It doesn’t seem like it should but who knows, lots of people did it.
