The problem sounds just like my car use to have it would turn over and catch for a second and then die out I noticed it did it most of the time when it was hot outside and the inside of the car got real hot. When you put your key in the ignition turn it to the accesories position and if you do not hear the click like the fuel pump turning on than its the main fuel relay (assuming you have some kind of honda or acura by your screen name)

 

have u changed the distributor at all???when i had my vtec swap done in my hatch it was done by autosolution(may that shop forever burn in hell) they put the wrong damn distributor in my car....it ran fine for awhile but they i would turn it over and it would sputter and die....it would backfire and not work....u may have a bad distributor

 

problem solved...im wrong everyone else was right, it jumped time =/