I attempted to connect to an experimental server. Battleeye updated itself and restarted DayZ.

I tried to connect to an experimental server and the same loop repeated. Battleeye did update itself, according to the time stamp on the files, but the loop repeated itself five times.

I went to ~/user/AppData/Local/DayZ and renamed the Battleeye folder to Battleeye_old.

I tried to connect to an experimental server. Battleeye updated one time and allowed me to connect and play on the first attempt after that final update. Everything is working now.