Some dovetail setups have a recoil stop for that exact purpose. Could make one by drill and tap a hole in base or ring into a divot into surface below/above?? Or, you might have incorrect width ring clamps for your dovetails?? - 11mm and 3/8" are not the same.
For clarity - your scope has inertia to stay still - the rifle underneath wants to buck rearward underneath it - effect is it looks like the scope went forward. The more I think about it, assuming that your rifle is a rimfire, the more likely the wrong size ring clamps - not much recoil from a rimfire. However, the Weaver T0-1 base uses "rimfire" sized clamp rings - on a No. 1 or No. 4 Lee Enfield usually in 303 British - you will see a "recoil stop" at very front of the dovetail - front ring is to be tight against that - scope will not move.
Ha! Thinking more - thought this was a simple thing - but now realizing there are many rifles with integral dovetails, of varying widths on the receiver, and in many cartridges - so if the above story did not solve the problem, might have to provide a bit more information about what rifle, what cartridge and what rings are you using?? Most all centerfire base and ring combinations that I am familiar with have some sort of recoil system - a screw head, a divot and stud, or a cross bar and slot. Is pretty much standard thing to push the ring's recoil contact forward, while snugging up the clamp. I do have some rimfire that rely only on the clamping force, though. And I presumed from your post that the rings are moving forward on the dovetail, not the scope moving forward within the rings.