my car used to do this.... check out the coil.. that might be it. thats what it was in my case. does the car seem like it misfires before it dies?? if it does then check out your ignition points and well, might as well replace them. they are like $2. the fuel filter and all are always good places to look too. i mean, how often do they really get changed ya know?
Run it until it dies- Have someone else turn engine over with key while you hold spark plug wire about 1/4" from contact with plug. If there is spark it's probibly a fuel issue. If no spark, then distributer cap, points, coil are suspects.
The obvious above is to put trans in park or neutral with emergency brake set for safety.
are you running a mechanical or electric fuel pump? probably mechanical check there as well a smal hole can cause a vacuum lock when things start to get warm. happened to me once took me forever to figure it was the problem.