Q: My car wouldn't start, but when I towed it to a mechanic to look at 2 days later they said it started right up. What could cause this?

I was driving my car for a couple of hours and then around 430 I went to my daughters house to pick her up. When we got in the car to leave the car wouldn't start. I would turn the key, but the engine wouldn't turn over. All my lights came on and there is no check engine light on. After about an hour I got it towed to a local shop with a good rating that I dealt with before for them to look at when they open up on Monday morning. I told them the same thing that I am telling you and the said they would look into it and get back with me when and if they find anything. Later in that morning they called me saying that the car started right up and they couldn't duplicate the problem. Do you have any idea of what could possible cause this to happen or at least give me some sort of direction to start troubleshooting? Thank you for you attention to my question and have a great day.

My car has 101382 miles.
My car has an automatic transmission.