Turn temp to 70
Furnace runs until 70 degrees
Maintains temperature for awhile - probably for a couple of hours
At some point it stops maintaining the temperature and keeps kicking on and off.
I've watched the thermostat - I'll actually turn the temp up to try to get it to kick in. The thermostat "flame" comes on, I'll hear it ignite, the furnace starts up and then runs for about 15 secs then shuts off. Thermostat calls for heat, igniter kicks in, furnace starts and runs for 15 secs then shuts off. So the Temperature isn't maintained.

When I get home from work it is like 58 degrees. I shut the heat off, then on, then the furnace will stay on. I go to bed and wake up in the middle of the night and the temperature is in the low 60's.