My Rheem AC and Robertshaw 9600 prog Thermostat (both 4 yo.) are not in same temperature. Thermostat NOT programmed. I manually set 80 when not home, and 74 when home. Two weeks ago problme started. Come home, room temp at 79, I turn thermostat to 74, I hear a click indicating that set temperature got below room temp, but AC does not turn on. ONLY when room temp goes up to 81, AC turns on, but only works until temp goes down to 78, then turns off. Keeps doing that all the time. Seems the tem range is 80 to 78. Does not listen to thermostat. I RESET thermostat and notice that default temp is 78 when everything is zeroed-out. AC still will not turn on if room temp below 80. Also, if I just switch from AUTO to ON, AC still does not turn on. Seems that thermostat is not talking to AC. Air coming out from AC (for that brief time) is very nice and cold, so not a freon issue, and not fan issue.. HELP.. it is HOT in Miami!!

Your manual folllow link.

http://www.icca.invensys.com/manuals...w/110-653b.pdf

You cannot calibrate this thermostat.

FAQ
Can I calibrate my thermostat?
The thermostat has a continuously self-calibrating circuit. A precision 1/2% tolerance reference resistor is used to continuously recalibrate the temperature sensing circuit once per minute.

I believe your thermostat is toast. You will probably need to replace it if your cannot get it working correctly after reading the manual at the link I provided above.

I called ROBERTSHAW and thye told me that if I hear the thermostat 'click' when I set temp below room temp, then it send signal to AC. But the AC is not receiving signal.
Right now, I realized, the AC works in the temp range 80 high to 77 low. When it gets 80, it turns on and cools to 77 and stops. So I cannot understand if problem is in thermostat, the AC, or the link between them!

The thermostat is defective. It should have a much wider range of adjustment.