Engine shuts off while driving and will not restart

Shut off. While driving today my car quit running. Then wouldn't restart. Now I've had that issue several times after going to a store or something, then coming back out the car would't start. It eventually always did. So this was new being I was driving when it shut off. After a few minutes it would start back up but shut off about a mile or so later. I noticed the green key light flashing right before it shut off the car. I did a hard reset by disconnecting negative cable on battery. Has been fine the last couple times I drove it. My question is, am I going to keep having this issue or should it be resolved? I replaced the alternator and battery a few months ago and that is when the once in a while thing would happen with not restarting after being out already. I don't know if that why the sequence was messed up or what. Please help with any advice you have!