I'm having the exact same problem with my hot water shutting off. I also have two separate valves. I haven't heard a clunk, it just diminishes hot water flow fairly quickly, with or without the cold water valve open.
The problem started some time ago, but the problem was minimal. I just replaced the cold water valve stem due to a bad valve seat, and now the hot water shuts off completely. The valves are old, I had to go to a specialty shop to find the right replacement. When I put in the new cold valve, I replaced the washer on the hot water valve and the screw appeared to be solidly in place. I didn't see any packing - is it possible my style valve doesn't have it?