Sounds like 1 of 2 things it could either be 1: the main relay which when it gets hot the solder joints seperate no contact means no fuel . or 2: the igniter which controls spark release and ignition coil control if it gets hot GOOD LUCK gettin your car started. have that replaced ASAP it causes more expensive problems down the road. My advice is have them both checked by an auto electrician .
http://autorepair.about.com/library/diy/bl_hmr-1.htm
http://autorepair.about.com/library/weekly/aa042603a.htm
http://www.markl.f9.co.uk/howto/electrical/main-relay/main-relay.htm