I have a Rheem Chiterion II furnace that does not always come on.
When the weather first turned cool I moved the thermostst up, the furnace came on and it ran fine, Soon after is turned off but did not come on again automatically after the temp dropped. If I slap the front cover of the actual furnace the pilot immediately ignights and the fan soon comes on, it will usually run OK for a whle but then repeats the same MO.
I did check the thermostat; it is OK.
The repair guy could not figure it out and naturally the furnace ran like a chammp while he was there!
Does anyone have any suggestions?

If it responds to "physical contact", perhaps you have a loose electrical connection somewhere, or the blower access panel is not securely attached, allowing the interlock switch to disengage.