heat exchanger blowing hot then cold

hi. i have a rpj natural gas heat exchanger. it blows hot air, warms up to the desired temp. then then the heat shuts off and keeps blowing cool air cooling the room back down. after i shut off the main power and turn it back on it works correct for awhile, sometimes days, sometimes just a few cycles. when it does the the light on the board flashes saying flame sensed with no call for heat. it has a luxpro thermostat with a cycle setting in it. i dont know if that has anything to do with it, but i figured i would mention every detail i know. also the vent coming into the unit for fresh air, there is no line going out, they ran a pipe for the exhaust going outside. apparently it has always been hooked up that way. thanks for any help.

cokebronco, to me it sounds like a problem with the thermostat.