Scope not holding zero - help?

I got my savage 111 combo yesterday. the older version with the no-name scope. I shot about 40 rounds through it today, and although i'm getting good groups, every time after about four or five shots the sight seems to shift, and my groups switch places on the target. For example, i had a 4 shot group directly below the center of the target, and then one "flyer" about five inches right and an inch down. Only it wasn't a flyer, the next three rounds landed right next to it. I'm not sure if it's the scope or the rings. I'd like to only have to replace the scope if possible, but I'm really not sure what to think at this point, considering I'm pretty new to rifles. Any help would be great, thanks.

Remove the scope, rings and bases. Reinstall the bases with loctite on the screws. Reinstall the rings to the bases making sure that the crossbolt all the way forward in the slot for each ring. Then install the scope in the rings making sure the turrets (not the reticule) are square to the action. Even out the gaps on the sides of the rings as much as possible.

If it is still behaving the same way after doing the above, replace the scope. Get better rings at the same time. I recommend Burris Signature Zee rings.

Alright, thanks. is there any budget scope you can recommend for a 100-150 yard hunting rifle? It's not long term, but atm I'm not having steady hours at work and something good for the money is what i'm looking for.

I'd pick up one of the Vortex Viper 2-7x32s from Camera Land. The Redfield equivalent is slightly less expensive, but the glass in the Viper is better.

Okay, thanks =]

A couple of other things to try are breaking in the scope by turning the adjustment knobs back and forth through their full range of adjustment until your wrist gets tired.
As far as decent economy glass goes burris has a $50 rebate on the E1 and bushnell has a $75 rebate on the elites. Both can be had for $150 or less after rebate if you shop around.

Mrcalamiteh

What do you have budgeted for a scope? Second, definitely use better quality rings and bases but don't put Loctite on the screws. I use a little bit of gun oil on the threads and make sure they are just snug.

Have you done a box test with the current scope?