Truck shuts off

I had my truck idling, while doing so my battery light came on. Then my voltage suddenly started going down. I tried driving it to see if it would help but it didn’t. It took my power steering my dash went black and the truck shut off on me. With a jump I was able to make it home so I assumed it was the alternator. I replaced it but the same thing keeps happening. It starts slowing shutting off. It still starts up when I don’t use it after a couple of days. What could it be?