It was solved today with the help of Aqara Support. They request to remotely connect and after a while asked me to try again. I did and it worked instantly.
I asked what the issue was, seems to be related to a token issue which they updated.
So if you have the same issue nothing much to do on your own but contact Aqara support and they should solve it.
Probably not helpful, but I just happened to have added and E1 camera a couple of hours ago. I added to Aqara app by scanning Aqara QR code then still in Aqara app on E1 hit the three dots for more settings in top right, then select Homekit and pair. Worked first try …
I had very similar issues with the E1 losing the connection in HomeKit after the most recent firmware update. Tried many things in different order with no luck. Last I changed the default name of the camera from Aqara Camera to Aqara Camera E1 when adding to HomeKit from the Aqara app and the camera has not disconnected in days. Prior it would disconnect over night or within minutes. I hope this helps others.
Update:
Went off line again after a few days of success.
I only rebooted my WiFi/Router this time and was able to add the camera.
Sorry for the false hope.