My central unit sporadically won't come on. It appears to be the thermostat, because unit cools fine when it comes on. I have replaced the stat twice and symptoms remain the same. When it does not repond, even the blower fan will not respond in "On" position.
If stat is good, could it be a wiring issue at the blower, or is there some type of control at blower that could be overheating? When unit won't respond for several hours, it mysteriously comes back on and works fine for hours/days.

It sounds like you may have a thermostat wiring problem, check the wiring from the thermostat to the furnace and any conections in the wiring to insure that they are tight.
When this happens if you go to the furnace and jumper(touch ) the green wire to the red wire that goes to the thermostat it should bring on the fan motor in the furnace, if it does then you will know that the problem is from the furnace to the thermostat, go to the thermostat and remove thermostat to expose the wiring and jumper these same wires if the fan comes on then you have problems in the thermostat.It is not likely that you would have the same problem with both thermostats.