That doesn't sound right. I have them on my desk. Don't even know where the bra case is. I use and charge them only once in a blue moon, perhaps every 2 months, and the battery does not die. I don't lay them flat or anything either.

Like others here, I don’t have this problem. I often leave them in my backpack for weeks between airplane flights, etc.

Have you reset your AirPods Max by holding down the non circular button until it starts blinking white and then reconnecting?

There have been times where the AirPods Max have sort of crashed, and I cannot get them to connect properly. I find that forgetting the AirPods in the phone/computer and then resetting them by holding down the button allows them to start fresh with a new state. Maybe that can help resolve the issue for you. But Im constantly switching them between three nearby devices so maybe thats why I have this problem. Just throwing it out there in case you haven't tried a reset.

Try hard reset (long press (~15s) both buttons).

I know I have had this issue and did not have it after reset. Though I do have another annoying, and seemingly unique issue: sometimes, when adjusting the position of the headphone, they do a “click” (and a loud one), and just shut down. After a few seconds, they boot up again.

The farthest from the last reset, the more often it happens. I have no idea why.