I don't have one of these devices..
The HDHomerun only works by IP address if the device is always given the same IP from DHCP server or the HDHomerun is setup with fixed static IP (or both).
suggests using the unique device ID..
Have you configured that device with fixed IP?
Are you sharing the HDHomerun tuners with other applications outside of "connected" backend ?
Maybe the problems relate to the random tuner ordering on reboot.
The soln to that is udev rules or modprobe options.
Are you using mythtv-setup to rearrange the tuners on a regular basis?
From a very limited use of udev rules:
modprobe options are simple & readable but not very flexible.
udev rules look more complicated than they are but have pedantic syntax
I would try to find a working example udev rule & use it as a template.
Interesting info here but don't blindly copy any cmds..