I've been researching this problem for the past week. What i've gathered so far is that some process interferes with mirroring after my phone has been running for a while... If I restart my phone, or chromecast - it works no problems. It also works casting netflix, youtube, etc. I have a samsung TV, and when i try to connect my phone through TV, it also works. I called Chromecast yesterday, thinking that it could be a defective chromecast device, but it works other than the above issue. So I think that some process gets activated some time shortly after phone reboot, and that's why when i press 'cast screen/audio' from Home app, it says 'disconnecting', because some other process is already working... I will be calling Samsung Tech support tonight, to see if they have any clue, although i don't get my hopes up. If their tech support guys are the same as their customer service reps, I won't get far with them.
I also tried any and all settings changes that i could think of, and nothing works. The best solution for me is either to restart my phone prior to mirroring, or just connect from TV to the phone (it works that way), not from phone to TV. If I figure out a solution, I'll try to update. I have a similar thread on Android Central in Note 8 General section that i started Sunday, 10/15/2017. No one seems to know the solution, and not many people have encountered this (you are the first person that i found with the same problem other than myself).
Just found this app by Samsung called "ScreenMirroring Patch", will try out after work.