we've seen the panel disconnect happen, but not very often. it's usually the switcher that gets stupid and stops accepting connections requiring a reboot. in our experience, sketchy network connections are to blame including bad/intermittent cables, not plugged in fully, or poor wifi performance.
as such, our equipment network doesn't have a router anymore, or any wifi either. just a switch (or usually more than one switch, each covering a specific location of gear). everything is hardwired and has a static IP address. this network only exists to control audio and video gear-NOTHING else. it may be more of a pain to setup this way, but it's WAY more stable.
we run a separate network for Dante audio. and a third network with WiFi for anything that needs internet. This means either more computers sometimes, or more than one network adapter per computer to get across different networks (like to control ATEM and stream from same computer). We have had excellent results with this setup though.
It also means more cabling sometimes too. that picture above has a 10x cat5 harness from table to control rack. so be it...