Have you check the fuel pressure, fuel pump, pressure regulator, etc.

Fuel pressure could be OK at start up then bleed off.

 

my apologies there is a crankshaft sensor on the 1mz, lmao its been a long day

 

JBandy, you should still verify spark/no spark when it dies and will not restart before you just guess at replacing parts. If spark ok then look to fuel. Fuel pump relay could be overheating and cutting out, or fuel pump.

 

soo my crank sensor idea still has some merit?

 

yeah possible, jbandy where are you from?

 

The same thing happened to my truck and it was the fuel pressure regualtor! I don't think that there is a way to test those, but I would put some good money on that being the problem.