http://bugs.winehq.org/show_bug.cgi?id=24059
--- Comment #7 from Phillip winehq@mrphlip.com 2010-08-22 09:49:17 --- A workaround: download the updates manually by opening C:\Program Files\StarCraft II*.torrent in a bittorrent client and saving the files to C:\Program Files\StarCraft II\Updates\whatever (if there's a whatever.part file in there, delete it). Then when you run the game, it'll pick up the updates from there instead of trying (and failing) to download them itself.
There only seems to be one update file that it's failing for... most of them it's able to get without problems.