I have a carrier furnace (17 years old) that quit recently. After wiggling a few wires, tapping here and there, I could get it to start up and operate for several days before it quit again. (it has electronic ignition). I can get it to work, but now it works only for one or two cycles (it's getting worse). Sometimes I can get it the pilot to light, then it shuts off. I try again and everything works fine. It seems to be the ignitor/lockout control (the part where the spark plug wire originates) , but the repair guy replaced that temporarily and it didn't SEEM to be the problem (my method to start the furnace is to wiggle and jerk on the wires coming from this part.) So he replaced the main gas valve (for 350 bucks) but the furnace stopped working again the next day. It never does the same thing twice - it seems to be possessed by demons.

Any ideas?

Does it have a thermocouple?

If so, I would replace that, they are very inexpensive and not too difficult to replace.

The pilot burner needs to be checked.

The pilot assembly is a heat activated switch and after 17 years is is possible that it is not reacting to the heat the way that it should. The way to check this part is with a OHM meter, in one position it turns on the electric spark and opens the gas to the pilot. As it gets hot the by-metal switch moves to make contact that turns off the sparker and opens the main gas valve. If this switch is not moving enough it will not make the contacts. The part is quite expensive so don't just change it hoping that will fix the problem.

If it's the old three wire pilot assembly(Green,Yellow,White wires) that's the way they act when going bad. The bimetal strip is sticking.