It may be too late for this, but here goes. I have a gas free standing stove that gets intermittant something like you're talking about. I'm suspecting the thermopile. Not the thermocouple. If that were bad the pilot would go out. If you can get to the wires coming from the thermopile where they connect to the gas valve, you should measure a voltage there of at least 500mv with the thermostat open. You may be right on the cusp and it's basically a crap shoot if the burner will turn on or not. I couldn't get the darn thing out. It's in there so tight I was afraid I'd break it so I just filed the side that faces the pilot and would you believe it hasn't acted up since!
Keep in mind that everything I said relates to a piezo ignition system.

Another obvious thing could be something as simple as cleaning your thermostat contacts.
Jim