Do you have a recoil buffer in it? If so try removing it.

Yes, I always use a recoil buffer. Like I said, I've had this gun for years and I've shot a gazillion rounds through it. It has never done this before. I'm thinking something has worn out. The magazine follower doesn't look worn.

Take the gun apart and place the slide release back into place, there is a ball detent/plunger that will hold it in place. Now simply slide a magazine in. You should be able to tell if the magazine follower is bent/warped or the slide release has been worn to the point that the follower no longer makes suffecient contact. Either is easy to fix, slide stops of all different styles are available at almost any gunsmith supply stores.

Ditto to slide stop suggestions. Have you checked all your magazines? As suggested in the above posts, check your mag followers. If the slide stop is in good condition as you say, then the only thing is the mag/follower problem.

Are you able to lock the slide manually, with an empty mag? And with no mag, using the slide lock?
If no, it may well be your buffer's too big, and won't let the slide come back far enough, but if that were the case, I would guess you'd have been having feeding issues all along.
Maybe your slide lock is wearing down, and won't catch the slide cutout.