I believe that when we re-run the program with the correct date and time, if the temp has to go up, the furnace runs until it gets the appropriate temp, then it turns off and when it does that, the thermostat also turns off going to the HOLD state.:confused:

Brand of thermostat?
Model number of thermostat?

White-rodgers
Digital comfort set II

I need the real model number to look it up. Usually a F110-23b or some such number. If not accurate I cannot help.

The model is 1F90-51

You need to take your thermostat out of the hold mode. Read all of this info about your t-stat.

http://www.white-rodgers.com/wrdhom/pdfs/instruction_sheets/0037_5099_B.pdf

I am also tossing in the install manual just in case you need it someday.

http://www.white-rodgers.com/wrdhom/pdfs/instruction_sheets/0037-5043rev_B.pdf

But when I run the program and the t-stat goes to HEAT, after the temp in the program is reached, the T-stat turns off and the status is sent back to HOLD.

I am sorry the directions did not help you. If you read and followed the directions to remove the hold feature and the thermostat still will not work to your satisfaction then the thermostat is probably defective and you will need to replace it.