Driving a few miles, engine cut out?

Driving a few miles, engine cut out. I was able to restart it a few times to go about another 1/4 mile in total, then it wouldn't start at all. I was running on empty, but the fuel light hadn't come on. Added a gallon, still wouldn't start. Had it towed; two days later mechanic got it to go 18 miles, no problem. Later in the day, drove another 20 and it died again. Gas at that point, per sensor, was less than 1 %. They added $20 reg, and it started right up. I've had it back for a week, no problem. Mechanic said maybe fuel pump is going, and I have to keep tank half full to maintain pressure; but he's not sure. He says there's no way to tell for sure. I'm nervous all the time that it's going to cut out again, and I'm avoiding highways.