Your issue is either clamp load on the screws or fit of the rings to the scope.
First, I would check the torque on the rings. To do that, tighten to a certain torque. Basspro says,"Most manufacturers recommend tightening base screws to 12-15 in/lbs."
Then remeasure that torque after 24 hours. It should drop less than 20%. Ideally, less than 10%. Then measure in 1 week. It should not drop any more.
Second, I would try lapping the rings. Improving this fit will improve friction and that should also improve torque loss some.
Last, I would try 4 screw or 6 screw rings as they will drastically increase clamping load on the scope.
On hard kickers, after torque testing proves the rings ok, I would final assemble with just a drop of locktite. The firing cycle will loosen good rings due to the cyclical nature of it. After you have proven the clamp load will stay, you want to make sure the screws will stay put.
BTW, what caliber, approximate rifle weight, scope weight, etc are we talking about. This advice would be much different for 22lr or 460 Weatherby!