OMG this was so obvious....
You know why it disconnects you guys? Because WoT replays must be played in offline mode :)
In the garage when logged in, all you can is to review list of replays with some details, but you cannot play, when you try to play it, it will disconnect you, to help it :) Once disconnected click on replay manager icon again (on the login page) and then you can play a replay.