Maybe something's going on with the fuel pump primer circuit when it gets hot? I.e. it's not keeping things primed/pressurized for those first 15 or 30 minutes after stopping.

Just to confuse things some more here are a few almost-certainly-unrelated data points of Hondas being curiously unwilling to start:
1) The S2000 (AP1 at least), when run completely out of fuel, will simply NOT start if you only add a couple gallons back to the tank. It literally takes about 5 gallons before it will finally agree to start.
2) The S2000 (AP1 at least), when spun on track, will stall as it comes to a stop *even if you got the clutch in during the spin*, and restarting inevitably requires 2-3 attempts (and maybe turning the car off and on with the key).
3) The '96-'00 Civic (EX automatic, at least, with D16 motor), requires progressively longer and longer cranking times to start when the fuel gets low (1/3 tank or so). The lower the fuel, the longer the crank time; when very low, 10 second cranks are common. The kicker: this is all *before* the low fuel light comes on, so there's still 2-4 gallons in the tank! It's worse when cold, but if the tank's low enough, it's prone to "catch-and-stall" even on a warm restart if you don't pump the accelerator just right. Again, this behavior is a "feature" of the car, i.e. they did it even when new.