I have a couple of M1's and I had one that may have been doing what you're talking about. If I understand the problem, you have a shell in the chamber but when you pull the trigger it doesn't fire.
In mine, I found that the recoil spring had lost some of it's oomph. When I would manually cycle a round into the chamber, the bolt would go forward but the locking head would not fully rotate and lock into the barrel, causing it to be just ever so slightly out of battery. You had to look close to see the difference in how the locking head was rotating. The firing pin would then not be able to go forward fully and contact the firing pin. It even happened a couple of times when the gun fired. It would shoot, cycle and then go click. I ended up changing out the recoil tube/spring assembly and I also changed out the original blued locking head with a chrome one. I have never had the problem since.
If you're looking to unload that 21" M1, let me know. That's my pheasant/skeet/sporting clays gun and I sure would like another. I've been looking for another 21 inch barrel for a while now but haven't had any luck but I'd buy a whole gun in a heartbeat.