Repeatedly getting message “Not Your AirPods Pro” and need to reconnect

Recently (since iOS 14.6?) my AirPod Pros have frequently lost their connection to my iPad and I get this message and have to reconnect them. Almost every time I use them.

On my iPhone, I usually get the message “AirPods Pro - You can temporarily connect AirPods Pro to this iPhone to share audio” even after reconnecting to the phone and using them. Sometimes, I have to re-pair them with my phone, just like my iPad.

Also, even if they do connect, often they are no longer automatically selected as the speaker. Instead, sound comes out of the device until I switch it.

None of these problems happened until recently. I used them with the same two devices, they would switch source automatically depending on which I was using, and I never had to re-pair them.

My AirPods are updated to the current firmware as are my devices (14.6). Both devices are using the same Apple ID and otherwise work together as expected.

Any ideas? Very frustrating.