Joe,
Sounds look you are coming to this from spingers
They are always shaking screws loose . . . .
The only "screws" that can mover over time and affect accuracy are the striker in the hammer and the spring pre-load setting. A little VC-3 in them is a good idea next time you have the gun apart. Other than those two, not much will move as you use the gun.
The one other related thing would be the shroud tightness - many of us have found that the POI (as well as repeatability) is very sensitive to the tightness of the shroud. I actually put a small silver dot on the rear of mine so that I can keep track of it, since it is easy to move as you handle the gun.
As for those flyers, if you can figure that out we will all be the better for it! That is what has been driving us nuts for years, although the problem tends to be the worst on the .22 caliber model. My personal view is that once you have ruled out the obvious factors (consistent speed, shroud tightness, pellet not clipping the baffles etc.) then the most likely answer is one of sensitivity of barrel harmonics to the pellet. It could be that weight variation is getting you as different weight pellets are in the barrel for different time periods - and if the barrel is moving, the POI will change depending on where the barrel is in its oscillation as the pellet exits. Some have had luck with simply tuning to a different speed, achieving better accuracy at a particular setting. Others have found good results from weight sorting pellets.
Good luck with it!