Faulty alternator! Most likely the regulator is suspect.
Most "rebuilds" try to use the original voltage regulator to save money.

The regulator is the #1 cause for failure. Unfortunately it fails first as you are describing. At high rpms under load. Followed by total failure.
Most rebuilders do not test their products to those conditions. Just under normal cruise conditions at a preset load and call it good.
I do know that Worldwide Products does. Each alternator they sell comes with a data spec sheet that shows the alternator's output plotted on a graph from 0 to 7000rpm plus.
Autozone & Advance carry this brand. Other's may as well???
NAPA, O Reilly's, Pep Boys, & CarQuest I know DO NOT! (Not that I'd even send an enemy to 3 of those places! NAPA's okay if you can get past their outrageous prices!)