Is the exhaust clean when it does finally start?

Or does the exhaust reek of unburned fuel?

If the latter, the engine is being "flooded" by a fuel leak and should
start if you press the accelerator while the motor is being cranked by
the starter. Such "flooding" can occur from one or more leaking fuel
injectors as one example. Flooding" doesn't affect a cold engine for the
extra fuel is needed to start a cold motor. Hot motors don't need extra
fuel to start.

If the exhaust is clean on start up the problem's cause may be electrical.

I had this car and I know exactly what you got... hot start problem. This is
because of fuel pressure loss and the fuel will simply turn into vapor with
hot engine.... vapor lock... which is why you can't start your engine
easily.

Two possibilities:
   Fuel accumulator shot... this is located above your fuel filter in the
back... one side is rubber hose... disconnect it and if fuel keep coming out
of it... it is bad.

   Compensator valve on the fuel distributor. It is the o-ring that
deteriorated... it is located directly on top of the fuel distributor...
with a hex bolt or a torx bolt... once removed, use something to pull that
piston out and replace the o-ring.