Have a 96 chevy p/u with TBI.  Will start cold and after running a very short time will die. Also if driven when you slow down it will die.
Sometimes it'll start right up mostly it won't.  If I shoot gas in it during a no start it'll fire right up.
Have check the fuel pump relay, the oil sensor and pump.  No error codes are in the PCM. Change fuel filter and under the advise a shop for $50 replace the coil???? What next?  

is it a vortec 5.7? this engine requires 85 psi fuel pressure to run correctly.  

It's 5.7 not a Vortec and does not run that high of a fuel pressure. Being a TBI it real needs 22 psi.  A local repair shop test the fuel pressure and said it was fine.  

Did you check throttle position sensor or the connection @ the distributor that controls the power to the tbi?