Since iOS 15.1 update on iPhone 11, AirPods Pro disconnect and have to re-pair with phone after 20 seconds

Since the iOS 15.1 update on my iPhone 11, my AirPods Pro disconnect (also gets forgotten from My Devices) and if I open the charging case the bubble appears "Not Your AirPods Pro: AirPods Pro not connected to this iPhone" with the option to "Connect".

After going through the re-pairing/re-connecting by holding the button on the back of the charging case, the AirPods successfully stay connected... for about 20 seconds. The iPhone then drops the connection and the "Not Your AirPods Pro" reappears. (It forgets the AirPods from the bluetooth list and I have to re-pair them from the beginning. Airpods do not show in "My Devices" bluetooth list).