No fuel spraying = Thats your trouble.
my GUESS - Vapor lock due to a low pressure fuel pump
Check your fuel pressure with a gauge - If low then check the voltage at your fuel pump connector. If the voltage is ok then lets talk about the fuel pump vs the fuel regulator.
Back in the seventies when cars were running mechanical fuel pumps and carborators this would happen kinda often. With electronic fuel injection, the fuel pump will pump more fuel than the engine needs. The fuel pressure regulator is located on the engine (In the throttle body in your case). Excess pressure/fuel is returned to the tank. They did that to get a consistant pressure at the engine.
This also fixed the vapor lock problem. Vapor lock occurs when the fuel in the fuel lines evaporates due to heat. Vapor lock occurs only after driving and then shutting down and "heat soaking" the fuel line. With the regulator and return line the vapor lock would be bled off and returned to the tank and cause no problems. Problem fixed right?
So if your fuel pump is marginal, it might pump enough fuel to run the engine, but not enough to return any fuel to the tank. When the heat soak problem occurs it just won't start when parked hot. Let it cool enough and the gas re-condenses and the car starts and runs fine. It could be a weak fuel pump, it could be a clogged fuel filter or low voltage to the fuel pump.
The fuel pressure test is the first item in diagnosing the problem. IF you want to go the route of just replacing parts, (NOT recommended) and the fuel filter hasn't ever been replaced, you could start there. It is however a great time to also check the fuel pressure on the 2.5 (which has no fuel pressure test point built in)
Also take a look at your fuel spray when the trouble is NOT happening. This guess is baised on the idea that you have fuel spray usually but no fuel spray when the trouble occurs.
Any chance under a sustained high load situation (going up an extended steep hill) that you also experence power issues?
[This message has been edited by phonedawgz (edited 06-24-2010).]