When adding a new display (chromebox) the process causes all my other displays to lose their display id. Using latest version of Rise and ChromeOs. This causes me to have to visit each display and manually reenter the appropriate id. Anyone else having this problem?
I think that might be your issue. If they're logged on under common credentials when you install the player on the new machine it's effectively re-installing it on the other machines using the same credentials. If you want to test the theory, create a new Google account and use that to log in on a new Chromebox. I'd be willing to be the others stay working.
Having said that, your setup is prone to being unreliable without the boxes being used under a managed domain and set to single app kiosk mode.