Sounds like it might be the thermo coupling. The tube that senses the pilot and shuts off gas supply, when pilot goes out. If yours is replaceable, it's Usually a $10 or so part. Unfortunately, some are not replaceable...

No, it isn't the thermocouple. The pilot light stays lit. It is still doing the same thing. If I turn it on it fires right up and works normally until it reaches temp but the next time it tries to fire up it hangs up. The power vent starts to go but instead of the burner lighting up it shuts down then tries again. Over and over. I disconnected the plastic tube that runs into the power vent and cleaned it out with a pipe cleaner. No change.

I had this problem with a furnace, try running the pipe cleaner in the orifice that the plastic tube goes on. I could hear the crud breaking up.

I had my power vent line plugged with spiderwebs, wouldn't let the system run. A few years later the control valve failed after 11 years, that was $400.00 cdn, ouch. The system would run for a few minutes and shut itself down.