So I was taking a look at my new, stock, unfired 1301 tonight and I noticed I have this problem too. Sometimes when there's two shells in the tube and I hit the cartridge stop release it'll throw one onto the lifter, but it's not always guaranteed, and it won't work for any other number of shells in the tube.
What really gives me a clue is that if I hit that stop, the lifter drops, but the latch doesn't fully swing into the position it does with an empty tube. When I push the shell in the tube a tiny bit forward so it takes pressure off the latch for a second, when I release pressure it works as advertised and the cartridge drops onto the lifter. So obviously there's something that's causing drag on the latch, probably the geometry. I'm wondering if somehow during recoil the inertia of the shells takes enough pressure off of the latch for the gun to properly cycle. I'm disappointed because my AL391 that I use for clays has pretty much the exact same manual of arms, and it's always worked like a charm. It's been one of my favorite guns to shoot and was part of the reason I got the 1301.
At least I know that by polishing that latch up a bit it'll fix things. Or maybe getting a stronger spring in the latch...