Quitting Brave Browser on both machines has, I hope, solved the strange issue of locking up the screen sharing. My last connection with a friend I noticed that anytime I made a remote click to his machine after about 30 seconds it would lock up the screen sharing. If I did nothing It would work for a while. Then I noticed Brave browser running on my friends machine and I we both quite Brave Browser. Worked fine for more than an hour when we finished. Whenever this lockup happened we were not disconnected or dropped, we were using the audio to talk while working and the audio always worked when the screen locked up. Hope this helps others.
Mac OS 11 on both machines