Keep getting dsiconnected

As the title says. In the last couple of days I'm getting constantly disconnected after several minutes of playing (Icecrown, Blackrock). First time it happened, I just restarted the client after getting "a character with that name already exists", and played just fine. But the next day I got disconnected several times to a point I was afraid to play my healer toon. Today I got dced several time in a matter of minutes, making it impossible to play. Do I need to redownload game client or something? Please, help.

P.S. I have stable internet connection and didn't change my computer.