Scope Mounting Problems
sygyzy,
First you need to determine IF you have the infamous "Bump" on the top-forward end of your receiver: [I suspect that you do...! !

]
Using a bright light on the far side of your receiver and scope mounting base, look for any light shining under the base...! ! IF you see any light under your scope mounting base, there is a strong possiblity that you have the "Bump"...! !
Next, remove your scope from the mounting base and set it aside. Carefully remove the mounting base. With a steel straight edge, lay it on the top of the receiver [front to back] and do the light test again. IF you have the "Bump", you will readily see it at the front end of the receiver. Dress-off the "Bump" with a file, following the instructions in Randy's Post [below]. If you are careful, you can remove the "Bump" and cover the 'spot' with your scope base...! !
Mounting a scope base on a 10/22 tips, The Bump
Now that the "Bump" has been dealt with, we'll move on to your scope and rings.
There is no way to exactly re-mount it the same as before. One screw too tight and you are way off.
What you are describing would indicate that your rings are misaligned with respect to the mounting base; so, if you tighten the front ring to the base first, the rear ring is tilted to one side, and visa-versa if you tighten the rear ring first; this puts a torque on you scope tube, and changes your POI each time you remove the scope...! !
0 Mark both the scope ring tops & bottoms with masking tape with an arrow pointing towards the muzzle; when they are replaced on the scope, the rear will remain the rear, and it will be exactly as it was manufactured.
0 Mark the scope ring locations on the scope tube with masking tape, so your eye relief will be the same as before.
0 Remove the tops of the mounting rings and the top half inserts; put the rear ring top, its insert, and screws in a jar cover; do the same for the front ring top, its insert, and screws in a second jar cover.
0 Now, mount the front ring bottom on your scope base, and 'snug up' the mounting screw. Check to make sure it is squarely mounted on the base...! ! No light, or equal amounts of light, should show under the bottom of the ring to base. Repeat for the rear ring bottom on your scope base, and 'snug up' the mounting screw. Check to make sure it is squarely mounted on the base...! !
0 Next, lay your scope in the lower halves of the rings with their inserts; it helps if the rifle is held by a padded jaw vise, or in your sand bags. Locate the scope fore-to-aft based upon your masking tape on the tube.
0 Set the upper half of your front ring with its insert on the scope tube; align the screw holes, and run the top half screws in only finger tight. Set the upper half of your rear ring with its insert on the scope tube; align the screw holes, and run the top half screws in only finger tight.
0 Check that your reticle is plumb and square with respect to the rifle; remember, the left side of the 10/22 receiver is flat, and a carpenter's square/level maybe placed there.

0 Using a 'criss-cross pattern', slowly tighten the upper half ring screws: right front, left rear, left front, and right rear. Give each screw about a half-turn, and then move to the next screw; repeat until the all the screws are 'snug'. Continue to check your reticle for plumb & square to the rifle.
0 Finally, tighten all the upper half ring screws using the 'criss-cross pattern' used above. Then, tighten the ring to base clamping screws.
0 You have mounted your scope in a stress free condition, and if you should remove it from the base, it should return to "Zero" when it is remounted +/- 1/2 MOA.
This should solve your most of your problems. If you still are shooting "low", check to see that you have the "pressure pad" [small bump of wood] in your barrel channel near the forearm tip. If not, try inserting a business card under the barrel near the forearm tip. If this solves the problem, it can be made permanent by trimming it so it doesn't show....! !
Hope this solves your problems...! !
Good Luck...! !
