When you say that you initialize the system, that's the remote you're initializing?
It sounds like you have a problem with either the thermostat or the control board.
If you can access the furnace while it's running, you can pull one of the thermostat wires loose and see if it shuts down. I suspect it will, because I don't think the problem is the furnace. But, it'd be a good idea to test it, just in case I'm wrong.
You could also do the same thing at the control board in the A/C grill. Find the furnace wires and unhook one of them and see if the furnace shuts down.
Salem 29RKSS Pushing a 2500 Mega-Cab CTD!
Gotta go campin!