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.

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

I noticed that behavior as well, but whenever I speak loudly with the headphones on. One remark to myself that's too loud, and suddenly pop and the noise cancellation is gone for like 10 seconds. Super annoying.

I don't have Max, but something similar happens with the AirPods Pro. See if you have "conversation awareness" and "hearing protection" turned on (both are on by default.) They're in the AirPods settings screen accessed via the bluetooth menu.

I'd suggest experimenting by disabling both and trying to repro. Then re-enabling the features one at a time.

I've never triggered it on the Pro by merely speaking loudly, but they're earbuds and farther from my mouth. What does trigger it for me reliably, is sneezing.

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.

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.

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