Hello,
I have 3 accessories (2 thermostats and one Sensiboo) exposed to HomeKit trough Home Assistant. My hub is a Apple TV HD 1st Gen.
I disabled the IGMP on my TP-Link and it resolved some of the “not responding” problems I got.
But I noticed that if I restart Home Assistant or change some settings the HomeKit integration seems to be reset. The devices are shown as not responding in the Home app and in HA I have notification for a new HomeKit bridge to be configured.
Yes, I experience similar issues, as does some others: HomeKit devices stopped working after iOS update (devices not responding) - #10 by Jimmy_Berglund
Not sure if it got something to do with my Proxmox setup, or if it is strictly an iOS/TVOS 16 issue. I did try and add advertise_ip in the configuration setup to check if this will make any difference…
homekit:
- name: HA_Bridge
port: 51827
advertise_ip: 10.0.1.105
Might be related, or not, but I am having difficulties adding family members to the newly configured home in Homekit.
Thank you. It worked for two weeks and then, out of nowhere, the devices are shown as not responding. The only thing out of extraordinary is an update for HA Core was available but not yesterday installed. 
Im having this problem too. How is this still a thing that HomeKit is not stable after a simple reboot, after several years of existing? Get it together!