I have 3 Savage rifles with the synthetic stocks . We all know these aren't the best stocks out there and there is signicicant movement of them out at the forend tip. I've found that it isn't so much how fast they are shot but were it is placed on the sandbags. I put mine about the center of the checkering.
If your mounts and rings are tight and this doesn't solve the problem, assuming it isn't you. I would then look to replacing the scope. Let someone else shoot your rifle if possible.