Yep, happening to me also.
Was playing my character, suddenly saw the red server connection error...then got dropped.
Every time I try and relog I get the trying to update the launcher message...then an Unable to contact the patch server. Please check your internet connection and if problem persists please contact tech support.
My connection is fine (all games, programs other than STO work fine over the internet).
Was hoping to play for a little before I had to run into work, but guess this will give me a little time to enjoy life away from the game.
Hopefully this won't happen often...or people might decide that real life is more fun than waiting for a game server to come back up.