Handleset or key cylinder
I'm sorry to hear that you're having trouble. There are definitely quite a few culprits for the issue you described, but the top suspect is going to be the mortise lock. These are probably the most common point of failure.
The good news is that it's fairly easy to test. What you want to do is take a smaller flat-head screwdriver and use it to turn the mortise slot that usually takes the key tail. Do it a few times to be sure. If it hangs up like you're used to, then the mortise is to blame. If it works fine without any issues, then we can safely rule it out.
After that, the source of the issue is going to be either the key lock or the thumb lever that's built into the handle. It would probably be the key lock, but for now test the mortise and get back to me. We can cross the other bridge if we get to it.
Hi so the mortise turned ok. Also the thumb turn turned ok with a flat head. I think it might be the key turn. I've attached a few close ups.
I wonder if the key spindle is long enough. When I put it back on the door it seemed to barely get inside the th7mb turn receiver.
That may very well be the problem. If the key tail isn't long enough, it risks slipping out of the slot in the mortise, which would account for why it doesn't seem to work half the time.
Either way, replacing the key cylinder definitely seems like the play. Your handle and mortise sound like they're in good condition, so they can be reused. My top recommendation here is the 82-310, but you should review our dimensions to make sure they all match up. It looks close to me, but you can never be too safe.
This key lock comes with an extra-long tail, too, so you have a little more leeway. I recommend cutting it down a little a a time, trying it out as you go. It will take a little longer but it will guarantee a proper operation.
You're very welcome! Best of luck on this project, and please let me know if you had any other questions. We're always here to help.