furnace does not fire up

I have Hail gas furnace with electronic ignition and Honeywell thermostat. 50% of time when the temperature drops to the fring level, the thermostat shous "system on", while the furnace does not fire up. Usually when this happens, temperature will continue to drop further until I go down and turn the main switch off and back on. At this point it fires up allright. Called service several time, they have no patience to wait until it happens, replaces the gas valve - no result.
Advice would be greatly appreciated. Thanks,
Roman
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You probably have a weak thermocouple. You can get them at Home Depot, but since you seem to be a newby on this, I think you should get a pro to check it out.
-john-
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