Don’t stand for this. Use the AppleCare you smartly bought because it was so cheap (you bought it, right? you bought it for a first-gen Apple product right? Oh bless your “frugal” self if you didn’t) and get your Max replaced, like I did, for this very annoying and dealbreaking issue.
They gave me a brand new pair, and the issue is gone. Still can’t ****ing update to the newest firmware though.
The culprit? I believe it was my Airfly Pro Bluetooth dongle that I kept trying to use with my Pros and Max. Both of them eventually had to be replaced and I swear it’s due to the Bluetooth dongle.