with any problem, it's always best to start with an assessment of what
the problem is and *when* it occurs.

1.  It only happens when the car has been driven and fully warmed up.
2.  The car will only start after it's sat long enough to cool off.
3. Something is getting hot enough to cause a short or other condition
that prevents the car from properly starting until it (the part) cools
off.

Hence, it MUST be something related to starting a hot car.

There's only a couple of things that it can be and I'm surprised that
your technician hasn't started diagnosing that.

1.  Throttlebody, either dirty or butterfly valve stuck closed. (e.g.
sensor is bad).
2.  Too rich fuel mixture when hot starting. (see above).
3.  Mass Air Flow sensor dirty or faulty.

Did your technician check the fuel pump assist or just the fuel pump?
Many cars have a second in-line pump that assists the fuel pump to
maintain pressure from the tank.  These are usually located further up
the fuel line from the pump.  If it goes bad, you can (actually will),
lose pressure, and the engine will run erractically..especially under
heavy accelleration.  It can also cause starting problems because
there isn't enough pressure maintained.