I has the same problem with my Savage 111. Found out that when I had takeing the barreled action out of the stock to do the initial cleaning I hadn't gotten it seated in the stock quite right when I put it back together. Try loosening both the front and read action screws, then push the barreled action down and back to seat the recoil lug against the stock and seat the action. Then tighten up the front action screw finger snug. Tighten the rear screw finger snug. Now tighten the front screw another 1/4 turn or so until good and tight, but you don't need to gorrilla torque it. Just tight enough that it won't back out. Do the same for the rear screw. Then try it again. You might also consider checking the scope mounts and rings to make sure they are tight too.

Mine would drift down and right, moving several inches. Last time at the range after I did this, it not only had stopped wondering but actually was shooting 0.83" average groups (at 100yards) with Winchester 150gr Power Points.

Mike