HVAC electric thermostat panel "goes dead" and then live again all the time
Sounds like a problem with the thermostat itself. Try replacing the batteries - and make sure you're using alkaline or NiMH batteries -- not "Heavy duty" (which drop off slowly, and are not good for electronics - or anything, really). 

If the batteries are good, you likely have a defective thermostat. See if they'll replace it on warranty (quick reading of the 1 star reviews on amazon say this can be a hassle) or buy a new one.