I've gotten kicked quite a few times myself in the past. There are several different fixes.
Fix #1First off you'll want to verify Arma 3's files((Arma 3>Properties>Local Files>Verify Integrity of Game Cashe)to make sure that nothing crucial is missing for the game. After that is done, start Arma 3 from Steam(not the Arma 3 Launcher)and start the campaign and let it run for 30-45 seconds. After that, try to log in to Beatnik Exile.
Fix #2Firstly, you want to go into the Arma 3 Launcher then mods and verify Exile and make sure it's up-to-date and isn't missing anything crucial. Then, you'll want to go into Arma 3 Launcher Settings(located at the top-right of the window)and update the launcher(located at the very bottom of the 'Settings' side panel). Then, log into Beatnik Exile.
Fix #3Go into Steam and start Arma 3. Then, go to your profile(located at the top-right of the Main Menu)and create a new profile. After that is said and done, start the campaign and let it play for 30-45 seconds then, log into Beatnik Exile.
If the issues still persists after trying the three fixes above, then I'd recommend getting in contact with an admin and seeing if they can help you out.
Good Luck and Happy Hunting!