The Model 302 Sterling has an "extra" spring that presses on the sear cam, called the sear cam spring. When the gun cycles, the blowback has to compress not only the barrel spring and the firing pin spring, but this spring as well. There's a delicate balance between the combination of these three springs and the power of the ammo you selected. Remove the sear cam spring and put it in your extra parts box. It is a flat spring that runs in a crudely machined channel and seems to cause more drag than spring action. The pistol will function perfectly well without it. Ninety percent of the time the pistol is not fully cycling, and this is where the problem lies.
While it's on the bench, remove the extractor and gently lap its sides on a stone or 360 Wet paper. Clean up the detent and spring hole and sharpen the extractor hook if you deem it neccessary. Lap the sides of the sear cam, and take the curse of the slide rails with a fine, single cut jeweler's file. Scrupulously clean the firing pin well, and polish the sides of the firing pin so it slides effortlessly in the slide. Polish the ramp if you're so inclined, and lube everything with Remoil.
Put the barrel spring on a mandrel such as a Phillips head screwdriver and gently weaken it on the belt sander. Also, the lips of the magazine should be symetrical and properly spaced; if you'd like, I can measure one of my four Sterling 302s and give you this dimension. I opened up the ejection port on one of my Sterlings with the milling machine to help it digest hollow points a bit easier, but this is usually unneccessary.
My Sterling 302s are 100% reliable, and digest just about anything with the possible exception of Remington Thunderbolts, which foul the barrel after a dozen or so shots. The thumb safety, by the way, is a weakness of these models, so I'd advise against carrying them with a chambered round.
Although these pistols bear an unfortunate resemblance to the Jennings and other cheap handguns, they are anything but. All steel and built like a tank, you'll not find a better and more reliable .22 pocket pistol in this price range---if you're willing to tune it up.