I've had some similar problems with Savage rifles in the past. The rifles shot great after I "tweaked" two things. First, check the screws in the base. They may be just a tad too long. If they are, the base won't tighten up. You may have to grind them down a very little bit. Second, check to see if the base on the front is sitting solely on the receiver. If the base is touching the barrel nut at all, it will create an interference fit on the base. In many cases, the Savage barrel nut is minutely higher than the receiver and "pushes" the base up in the front. If this is the case, bevel the front edge of the base so the base cannot contact the nut. Been there, done that, and it worked to correct the problem. I'm positive that if this doesn't correct the problem then you need a new scope. Also, ditch the cheap rings and get a set of Warnes, Burris, or something of similar quality. Good luck.