Jeep Liberty 2002 won't start after short trips

My Jeep Liberty 3.7 won’t start after trips of about 1.5-2 miles. Longer trips are fine. It acts like it’s getting no fuel – the engine turns over but it won’t start.



If you let the car sit for about 45-60 minutes after you discover it won’t start, it will start right up!



Any ideas? We have to leave it running when we go to day care!



Also --the engine light is usually on and steady during these times. Does that provide a clue?