I have an old Burnam Gas furnace and a gas water heater both connected to a power vent and a bunch of sensors/control units.

My furnace shuts off during the night. The weird thing is I can get it working again by running the hot water! Can anyone speculate as to what the problem is and how to fix it. I have had 2 repairmen come in and they didn't fix it. The thermocouple was changed out and some of the control wiring was re-wired but this still happens!

The weird thing is I can get it working again by running the hot water!
Could you tell us what you mean by that/

Does that mean that you can't relight the heater until you run some hot water?

I assume that the heater has a standing pilot lite and it goes out when the heater shuts down. Buy "getting it going again" I assume that you can relight the pilot after running some hot water.