Random Engine Power Loss

[Mazdasweed34]

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Year/Make/Model: 2007 Mazdaspeed 6
Mileage: 150300
Location: Colorado
Concern: My Mazdaspeed6 will randomly stall while driving, but only on hot days. The car will be running perfectly fine when it suddenly loses all throttle response, the engine shuts off, and the RPMs drop to zero while all of the electronics remain on. After stalling, the engine cranks normally but will not start for approximately 30 minutes. Once it has sat and cooled down, it usually starts and runs normally again. Not sure what it could be the in tank fuel pump is pretty new. Also when it happens my coolant temps aren’t high. Any help would be great.
Modifications: all SURE billet mounts, SURE intake, Overspeed injector seals, Autotech HPFP internals, AEM 340iph, Billet T case caps
ECU/Tuning Software: Cobb Accessport V3
Tuner: Stage 1 Cobb tune
Is the concern intermittent? Yes
Can you duplicate the concern? No
Recent Repairs: HPFP seals
Correction:

 

[Easter Bunny]

Can you post a lot of it happening

 

[Mazdasweed34]

Can you post a lot of it happening

I could try but it is so random when it happens. The only constant is that it is hot out. I forgot to mention that the coolant temps are fine when this happens.