Car dies after it warms up

The first thing I would probably check is the fuel pressure (during the failure) and see if that is maintaining spec. We have a Saturn specialist here that may check in and have something specific to add.

Hey wrenchtech you called lol the first thing I would check is the coolant temp sensor it sounds like the engine is flooding out getting too much fuel. Most of the time on those cars when you have to hold your gas pedal to the floor for them to start or try to start its a bad coolant temp sensor. Very common for them to fail I think I have replaced 3 or 4 co far on my 1999 saturn I own so far. Also inspect the inside of the coolant temp sensor connector if the terminals are green or blue instead of silver then you will need to replace the connector as well. The sensors crack and leak coolant into the connectors corroding them. Let me know what you find but honestly I would just replace the sensor there under 20.