my daughters jeep has this strange problem where it will just shut off when she's driving it. After 15 min or so it starts right up until it shuts off again. My question is, could this be a sensor in the air intake, like a throttle position sensor or some such? Or is it something else?

 

Buy a manual and follow the procedure to test the Crankshaft Position Sensor. That is the most likely culprit on a ZJ. You will need the manual more times then one so this is a great reason to buy it. The sensor runs about $60 at most part stores. I recommend the one from Pep Boys.