Car just shut off without any warning

My daughter was driving at freeway speeds and the car just shut off. Replaced the fuel pump, still does not start. Timing belt has about 500 miles on it. Not sure what to check for.

I started the car and off I go, 5 minutes later while accelerating on the 4th gear, the car gradually losses power and stalled. Previously, it happen like once a month but for the past three days it happen once a day. Before this I can start the car again after waiting about 5-10 mins. However last night the car would start but immediately dies off and stayed like that for one hour. I was only able to get the car running this morning. I would be really greatful if I can get help from here. Cheers!