iPhone randomly disappears from Audio device list

It sounds like a network issue of some sorts. As it is your network and your device(s) the hard work of troubleshooting is primarily yours. If you hope for help from the community you may have to come-up with something others can go on with.

This may currently look so but out of experience it usually isn’t the case. Try to find a pattern looking at logs (router, core machine, phone) and usage patterns of other, potentially unrelated looking software on all of your devices. If you want help from official support, please create a thread in the support category of the forum (read also: I'm having a problem with Roon -- how do I report it?).