OP, there could be a number of things wrong with your rifle.
First, is the magazine well original to the rifle??
The original magazines were plastic.
The mag wells were proprietary to those magazines and it was difficult to make any other magazine work.
The original plastic magazines had problems with the lips breaking off and cracking. I still run across a few of those, that were relegated to closets because no one bothered to make replacement magazines out of metal or plastic, that would fit into those rifles.
After about ten years, Cooey/Winchester/Savage came out with a different magazine well, that only accepted proprietary POT METAL magazines, that were quite distinctive in their shape, which looked more like an old style skeleton Key and slot.
This new magazine/mag well design was adaptable, without much effort to the original rifles.
If the installation wasn't done properly, feeding issues were the norm.
Then there is the type of metal they used to sinter the pot metal to shape those magazines. It wasn't the best quality and wears very quickly.
Several different companies bought up the rights to manufacture the Model 64. They all did it on the cheap and none of their magazine issue fixes were really successful.
They're sleek looking, attractive rifles that are well balanced, accurate and a pleasure to plink, target shoot and hunt with, when they're functioning properly.
IMHO, with a different magazine system, they could easily have given the Ruger 10-22 a lot of competition on the ranges as well as in the gun shops.
My very first semi auto 22 rimfire was a lovely Cooey Model 64, in a nicely figured Walnut stock with pressed checkering and a rabbit on each side of the palm swells.
It was quite an innovative marvel at the time. They used plastic for the magazine, magazine well and trigger guard. The plastic 60 years ago wasn't nearly as advanced as it is today.
I saw a magazine that was made up on a 3D printer, to fit the original mag well of the 64. It worked well and was made from a slab of DELRIN
With GOOD, properly mounted, functioning magazines those rifles will feed any bullets, copper plated, lead round nose, hollow points.