Chevy Aveo Multiple Alternators Failing

Soon after I got an engine replacement in my 2009 Aveo, the battery and brake lights would come on and the battery would read below 12 volts and not be charging. We've had a similar issue on another car so we replaced the alternator. Worked great for about a week, then same issue. Took it to a shop and told them it was a brand new alternator. They tested the alternator and said it wasn't putting out. Got a new alternator put in. A week or so later, same issue. Took it to a shop I know better and told them this would be the third alternator to go out. They replaced the alternator. Two days later, same issue.
Now, we can fix it for about a week by disconnecting the battery for several minutes. I believe it's a computer issue, but no one will do anything but replace the alternator and four alternators later I am certain it's not the issue.

Can someone please help? I've already invested over 6k into this car.

There are pretty much three possible causes going on here. I’ll list them in the order of most likely (in my opinion).
1) Crappy quality rebuilt alternator (Autozone is the worst offender, but there are many crappy rebuilders). I would recommend a used alternator from the junkyard before I’d put one in from Autozone or Advance Auto.
2) Your battery is past its useful life and the alternator is trying to charge a battery that won’t take it, causing the alternator to fail quickly because it’s beating itself up trying to put a crapload of amps out to the battery.
2.5) a combination of 1 and 2.
3) corroded wiring, bad grounds in the engine compartment, bad 12v connections at or in the fuse box, or possible ECM issues (doubtful).

I'm assuming that your battery does not discharge overnight indicating that you have a parasitic draw.

I do have a new battery in it. It and the old battery are giving the same issues. How likely is it that four alternators have a bad rebuild?

Unlikely, but still possible if they are “economy” rebuilds like Autozone, advance auto, or cheap china made.