Well, it's not likely that the compression changes from start to start, so it's down to fire or fuel.
Be more specific about "cranking it several times". Does that mean cranking for 10 -15 seconds with no fire, resting for maybe 20 seconds, then cranking it again for 15 seconds? When does it finally start when warm?
Do you pump the gas on the warm start? What if you don't? If it cranks a time without firing, I'd pull a plug or two and see if they're wet or dry - too much fuel, or too little. Does choke make a difference?
For me, fire is a little harder to diagnose, and seems less likely. You hear about coils or condensors that have increased resistance when they get warm - it seems like this would present when it was still driving though.
Could be down to a loose or corroded connection in the ignition circuit, say, at the key switch, ammeter, etc.
But I'd guess fuel first. Percolation, as Scott said, definitely a possibility - so is fuel seeping past the float valve and flooding the engine, though you'd likely smell that . . .
Just some thoughts - hope they help.
-Michael