Fuel pumps can fail slowly. They'll freeze up for a while and then cool down (or can be knocked loose) and then work again 'till they heat up again. You should definitely keep an eye on the fuel pressure and if it seems low, it may be that the fuel pump is bad. Or you could have an electrical fault somewhere that is stopping the pump. Check your various relays/fuses etc too. One thing is for sure, if it will crank but there's no pressure at the fuel rail, then the reason it won't start is that there's no fuel to burn. The question is, is it the pump itself, or is it a fault before it. Hard to say without any more testing.

I have heard of all of the following causing stall/no start

emissions/erg stuff
crank/cam position sensor
fuel pump relay
fuel pump inertia switch
bad ECM
bad coil pack/ignition module

there's a lot of stuff to check