I have a 2001 Hyundai Accent 1.6L. While driving it wil die, there is no spark but all the fuel pressure is fine. After it cools down it starts and drives for about 5-10 miles then dies again.

Was it running before you worked on it? If so, double check your work.
Make sure battery has a full charge and battery connections all good. Did you check good voltage and ground for fuel pump motor at the wiring connector?
If it cranks good but won't start, have a helper crank it, while you check for spark at the spark plugs. If spark everywhere, use a gage and check proper fuel pressure, I don't care if the pump is new, check fuel pressure, anyway. Also, check fuel injector pulse. Only crank the starter motor a few seconds at a time, let it cool off.
Are there any applicable trouble codes? How long since over-all tune-up?

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You'll have to figure out if it is a fuel or ignition problem.
When it quits running, quickly check for spark at the plugs and fuel pressure.
Is the check engine light on ? Have you checked for trouble codes ?
It could be a relay, the ignition module, coil, fuel pump, or a list of other things.
Generally, a problem that occurs hot then goes away cool is an electrical part that is failing.

Replace the throttle position sensor (TPS) (since you've checked/replaced anything else which could be causing this problem - except WIRING). Reinspect all wiring & connectors/connections before replacing the TPS. Also, I've seen (on occasion, a faulty "Main Relay" create the condition you describe). Suppose you have a faulty ignition switch (ignition key). When placed in the 'START' position, the engine starts normally, BUT, when you release IT to the 'RUN' position, the engine dies - CLUE?

When your driving say about 20 or 30 minutes, the car, no matter what, just dies. If the engine cools down, it will start and run just fine, for about another 20 or so minutes, and same thing? Change the coil. its bad, it over heats, and pow. when it cools, works great. Had that happen to me. hope this is the problem

remove one of your spark plugs and have some one turn it over you stick your finger into the spark plug hole if compression pushes it out then its not your timing belt if it doesn't push it out than replace your timing belt

#1. Scan for trouble codes. If any, record them and let us know which ones they are.
#2. Connect a fuel gauge to the fuel delivery line at the engine... try to start the engine while monitoring fuel pressure... if there is fuel pressure (approx 35 to 50 lbs), the problem is elsewhere.
If no fuel pressure, check fuel pump relay, fuse, wiring to fuel pump connector (power & ground - use 12volt test light). If power & ground are present, problem is the pump (fuel filter is attached to the fuel pump inside the tank).
#3. Check injectors for injector pulse, check ignition coils for spark to spark plugs.

check to see if you have fuel pressure after it dies. fuel pump could be getting hot and shutting off.

I had a similar problem and had an engine tune up done and the car runs almost like new now. Mine is a 2001 Hyundai Accent too.

I had the same problem. I found out that the fuel pump was not putting out enough pressure. changed the pump and bam down the road I went.