seems the original question needs repeating for clarity. What you've asked seems extremely vague, even if, as you said later, you posted it in the 'target and precision rifles' subforum. Rimfire or centrefire? (CF)
at what range to your preferred target?(matches are from 100-1400m)
what do you mean by an 'acceptable zero' - are you referring to something like 'how close to actually putting your bullets in the centre of the target do you consider adequate?'(yes)
or more along the lines of 'where do you zero at whatever given range, such that holdover is necessary, or not?' (yes, normally dial for elevation, but some cof with multiple targets on the clock require just using holdover)
i am finding this phrase especially difficult to understand. To me, an acceptable zero is one which will best result in stacking my projectiles at the desired point of impact, with whatever adjustments made in crosshair placement for wind, and whatever holdover adjustments as needed for different ranges outside my normally preferred zero distance. To 'achieve/confirm' a scope/rifle zero one shoots groups(how many, how many rounds) from a good rest and the groups of holes left on paper are enough to either confirm zero, or to indicate further reticle adjustment is required to obtain zero. Could you clarify the intention of your question?
As for 'does it change/what do you do about it?' - this seems almost to be begging the question regarding equipment quality and/or installation integrity. If i had a firearm which shifted zero from one session to the next, i would examine every component involved, from the rail to the scope mounts to the scope itself, and try to determine which was defective. Aiming tools which result in inconsistent points of impact would not be acceptable in any circumstance. Again, it seems unclear what is being asked. Are you trying to shoot accurately using a $50 scope, or $20 mounts,(again in tr and pr forum so no)
or is something loose, perhaps your barrel? Very puzzling.