Rule of thumb, scopes that come with new guns are cheap, and most often, scopes that you buy on used gun are too, guys don't leave a great scope on a rifle when they sell it.

Your BSA is cheap, i know this from experience. They are NOT good quality scopes, .22lrs' don't usually have much recoil, so you can occasionally get away with a cheaper scope, but I have known them to be fairly poor quality and for the zero to shift even on a .22lr. Go to walmart and look around, the fixed 4x32mm like yours would sell for around $20, if it's even that expensive, and it's certainly not worth that!!!! I've got a BSA .22lr scope in a drawer somewhere that the recticule lens broke loose in, tip it up and it slides to the eyepiece, tip it forward and it slides to the front again. A scope body doesn't have to move for it to shift zero, the internals are the problem...you can have the tube clamped so hard you're warping it and it doesn't mean that the scope isn't shifting...Are you using the Ruger rings that came with the rifle? If not, what mount did you use?

If your problem is flinching, you're likely in trouble, since you're learning it so early, and the fact that you're doing it with a .22lr doesn't speak well for what you WILL do with a rifle that actually recoils.

Knowing the 10/22, and that you're a beginner, it's not the gun, and assuming that the scope ISN'T moving, it's most likely you. Practice a bit and you'll improve, but you've got to practice correctly. 300rnds isn't even a day's worth of shooting for a .22lr, let alone 6mo's worth.

What ammo are you using? Any given bulk bullet isn't made for 40-60yrd shooting at squirrels, this range with that kind of accuracy is a pretty good reach for a beginning rifleman, I've hunted squirrels since I was 4 and I don't know that I've ever HAD to take a shot that far...I get about $20 worth of free fishing lures every year from Mepps from selling the tails, $0.18 a tail, you do the math, you don't have to take long shots, and asking that much from a beginner with a 10/22 with a bad scope and poor ammo, 25yrds is asking a lot.