Rich, it sounds like it still needs a good cleaning. My clock in my '48 was running fine and keeping good time, but would occasionally stop. That's a sign that some type of dirt or debris is still in there causing it to stop - it doesn't take much to stop the intricate gears, just a tiny speck of dirt. Sometimes a tap, or in your case, removing it, makes it start again.
I'd contact the person that worked on your clock and tell him about it. It would depend on how long it's been since you had the work done too. Like a mechanical watch, your car clock should be cleaned and oiled periodically also.
Owners of vintage mechanical watches know that you should always keep your watch/clock running, regardless of if you're using it or not. If the clock sits, the oil starts getting gummed up and can also cause it to periodically stop.
I took mine to a local clock repair shop and he said it looked as if hadn't been open and cleaned since 1948, but that everything otherwise looked good. He gave it a good cleaning and oiling and it hasn't stopped since. I TRY to keep it wound up, even when I'm not driving the car, but admittedly, it's easy to forget if you're not driving everyday.
I've never used this service, but Smith's Classic Car Clocks provides a reconditioning service for $60, which is cheaper than I paid for my cleaning. Maybe others on the forum have used him?
http://www.smithsclassiccarclocks.com/default.asp
