Your scope may be on the higher end for quality, depending. As was posted above there can be slight changes with impact with different power settings, shouldn't be that way, but it is very possible. This would be less so with a higher quality scope.
I try to do my final sight-in at a power close to what I will use for most hunting. That said I'm not afraid to adjust the power if called for.
The same goes with 'adjustment clicks', cheaper scopes aren't going to go 1/4" at 100 per click, or whatever. Yes they should adjust, but it may not be anywhere near an exact relationship per click. It also may take some recoil after adjustment to 'set' the adjustment.
Once in a while you see an article in a gun mag about 'shooting the box'. That's where the guy runs the adjustment though a box pattern, then ends up back where he started. A high quality scope will end up back where it started when adjusted back to original. A cheap scope won't make it without refinement.