AMEX ended relationship - can they get one back?

I tried asking a customer service rep and they weren’t helpful but, my brother isn’t sure if he can get a card again and I wasn’t able to find out anything useful.

TL;DR - he carried a hefty balance but was making payments on it while not adding much more on to it. I only saw one late payment; been a Gold then Platinum holder since 2013 and was always in good standing. Then I think it was august of last year he gets a letter saying the card was being canceled. It still had a $3k balance on it at the time of cancellation but that’s since been paid off.

So question is, can he get a card again? Or is he blacklisted?

I told him at this point I don’t think his credit is good enough anymore (sitting at 720 right now…) so he likely has to wait to get that back up. But I wanted to see what y’all thought.

Many thanks