I have had the same issue on/off for the past 4 months.. I have a Windows 11 Pro setup on a DELL XPS 9520 laptop.. I have tried EVERYHTING to fix this.. from hardware resets, to complete removal and reinstall of BT drivers... I thought the issue was with the Intel BT chip in my Dell laptop.. but even when I used an external USB BT dongle I have the same issue.. mic appears and then after a few minutes it disappears.. this is happening on 3 different BT headsets.. Apple Airpods, Sony WH-1000XM3 and Beats BT headset..
I had DELL replace the motherboard on the laptop.. same issue.. so clearly this is not hardware related so more than likely either the core OS (Windows 11 Pro in this instance) or perhaps a driver issue.. either way Microsoft should be stepping up here and investigating this. I have followed standard RCA practices as I am a software engineer and can't find out what the issue is.. this is either a broken windows patch or a BT driver issue would be my educated guess.
Paul