Player AR-Emerald is losing connection
Player AR-Emerald kicked off by BattlEye: Missing OS Privileges (Run game as administrator)
That's what is in the logs bud. The first one could be almost anything since it doesn't give any reason. However, the server maintained running so I'd have to guess it's a client side ISP/Network issue first. Please submit a tracert and run WINMTR while connected to the server to help narrow down possibilities.

WINMTR can be found here,
http://winmtr.sourceforge.net/