it sounds like your fuel pump. When a fuel pump starts to reach the end of its life, it will usually fail when it gets hot. And by that i mean it works fine when you first start it up and go for a drive. BUT, drive for 20 minutes or so (the pump heats up) make a quick stop and then it wont restart .....because the dieing fuel pump has overheated. Give it 20-30 minutes to cool off and it'll probably restart and the cycle repeats. Eventually the pump will fail completly so replace it now while your car is in the driveway. its a pain in the ass but you can do it yourself in an afternoon...... but if it's your first time droping the tank give yourself a day/weekend just to be safe.
Edit to add. the worst part is connecting/disconnecting the 2 hoses from the fuel delivery pipe/vent, the rest is cake.
[This message has been edited by DLCLK87GT (edited 01-17-2015).]