after it shuts down and refuses to start test 2 things, one check for spark, and two check for fuel pressure at the fuel rail, that will tell you alot about your problem.
to check for spark keep a spare spark plug on hand and when it dies pull any 1 plug wire off the spark plug in the block and put in the one in your pocket, leave the end of the plug on a metal surface in the engine compartment, have someone turn the engine over and watch for a bright blue arch between the electrode and the bottom of the spark plug.
if you don't get spark there, then remove the end of the coil wire from the distributor cap and try your spare plug there, again have someone turn the engine over and look for spark at the plug.
if you do not have spark there then you have an ignition problem which we can trouble shoot later.
DO NOT HOLD ONTO or TOUCH the PLUG or WIRE while checking for spark. 10 000 volts wont **** you but it hurts.
for the fuel pressure test all you have to do is buy a fuel pressure gauge from the parts store, I think they go for around $30, it connects to a schrader valve on your fuel rail, which is the same kind of valve as on your tires. with the gauge in place turn your key to on for a couple of seconds to let the fuel pumps to run and check the gauge.
if you dont get a reading on the gauge then you have a no pressure problem, I have a thread in the how to tech forum on how to diagnose this problem, but let us know how your tests go and we'll get you the info you need.