I also must restart openHAB after a reboot of my Fritz!Box 6660 Cable. Unfortunately there currently seems to be a bug in Fritz!OS 1.14 which makes this necessary every couple of days. Basically the box runs out of memory. First the web UI stops working and then the internet connection goes shortly afterwards.
(German language version only, sorry.)
Even before that the Box would occasionally reboot. Possibly due to problems with the cable or by remote command of the provider. (My box is not branded, but could still be controlled remotely.) No matter what the cause, openHAB gets unusable afterwards. I can see that activities like item state changes are still being logged continuously. But the Fritz! actuators are non responsive and many errors related to the Fritz!Box being unnreachable are being logged. My HomeBridge installation seems to stop working as well, although I configured everything by IP address (not alias).
It is really hard to tell what exactly goes on, but it strongly points in the direction of the Fritz!Box bindings. So much so that I am considering to stop using the bindings for a while to try to isolate the problem. I currently using the “AVM Fritz! Binding” to control a couple of smart home actuators and the TR064 binding for presence detection.
Edit: openHAB 2.5.3