Since a buddy of mine had a POA change with a $1500 Nightforce scope when changing between magnification levels (so it isn't always just the cheap scopes, unfortunately), I checked my variable magnification scopes to see if there were any issues and found none.
It goes to reason that if you are going to attempt to humanely take an animal under given parameters, you should first check to see if the equipment will perform accordingly before the hunt.
Curtis, you can easily verify if you have a problem by going to the range. If you think your POA shifts when you zoom the scope (which will result in a perceived POI change to you since altering the scope doesn't change the POI, only the POA), then you may have a bad scope. If you aren't certain how much of the problem is being caused by the scope or you, or if you can't consistently produce a result, then get an experienced shooter to work with your scope as well. It will help to rule out YOU as the problem. After all, once in a while, everyone has a bad day where they can't get things to work correctly.