Well you only need three things for it to fire, fuel, air and a spark. Getting air is pretty much a given so......
Are you getting a spark when hot. Maybe get an inline spark plug tester and throw it in there when hot to see if you are getting a spark
If no spark then I'd suspect heat soak affecting the coil and/or ignition module.
If you have a spark then it's gotta be fuel. Check you have fuel pressure when hot/not running. turn on ignition (do not start). pump should run for a couple of seconds then turn off,. Take a rag to stop fuel spurting everywhere and depress the schraeder valve in the fuel line, Pass side of engine by intake manifold to see if you get fuel. Be careful it may spurt everywhere and fuel and a hot engine are not a good mix, hence the rag.
No fuel. Check the pump does actually run when you turn on the ignition, you should be able to hear it. If not I'd track that down, maybe bad relay (affected by heat?) or pump itself.
If you have fuel, why is it not getting into the cylinders (injectors?)
Well that's the way I'd go at it.
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Anything I might say is probably worth what you paid for it, so treat it accordingly!
Dave
www.ltlfrari.com
