How do I diagnose a thermostat and HVAC that intermittently doesn't respond?
Check the pressure valve - we have been having this exact problem; my father took one of the hoses off of one of the pressure valves (mine has 2) - blew into it to clear a blockage and it worked fine again.

Last week when this first happened, the technician did the same thing, so blowing on the hose looks like a temporary fix (although they blamed it on the thermostat, which isn't the case)

The difference being my furnace is a 9 month old Lennox SLP98V...

If theres a problem with the pressure valve, it can prevent the burners to light up or stay on. In our case, the furnace would rev up as if it were gonna turn on, but then die. it would try this about every 5 minutes.

Hope it helps. I'm about to flip out on my install guy.

-Mario