2001 ford expedition, turns off after running a while.

Have you changed Fuel pump relay, or plugs/wires?

In situations like this ignore useless advice and simply run the fault codes . Check for cam/crank position sensor. check that the immobiliser is operational--- check that the cam shaft is turning(broken timing belt). It will all depend on the codes

Try changing crank sensor and cam sensor helps with electricity running through engine

Cranks and not turn over,you need fuel pressure, and you need to have spark at the sparkplugs,when you crank it do you hear the fuel pump humming at least?This is a good place to start crank it and listen for the fuel pump,you should at least hear it when you turn the key on

When electrical component such as a crank position sensor or even a cam position sensor warms up it develop high resistance. That why if you let is sit that component cools off and resistance becomes low.You have a ignition control problem this stem from ICM (If equipt) to cranksensor to camsensor,

that is my first thought the fuel pump!

Does you fuel pump delivers fuel. Is it there a spark.

hope in turn key on not to crank or start you should hear a grunt sound that is fuel pump no grrrrr sound no pump!!!!

The profile ignition pickup is the cam or crank sensor

These things had serious problems with crank sensors. There was even a recall on them. If you can get ahold of code reader and check it and it has any type of crank or cam sensor code replace it. Ford now sells them for under 50 bucks. If you slide under the vehicle and look toward the pass side of motor right above the crankshaft dampner on front of motor you will see a sensor that has a metal bale on it and one 10mm size screw holds it in. Remove the connector, take the 10mm bolt loose with a 10mm 6point socket so it dont strip. Then spray some penetrating oil on it. Grab some channel lock pliers and work it back and forth till it comes out. Reverse to install be sure lube the oring with oil before installation. We keep cranks sensors in stock now.