I've also been getting the Steam Authentication Error like other players. I've been periodically trying to get back on with no avail. However, I've noticed that Hours Played is still increasing; albeit not for the same amount of time I've been off.
Maybe the Steam Server still sees some of us as still being on Spiral Knights eventhough we've logged off and re-installed Steam?
IGN: Hmeister
That steam only counts the time that the client is actually open, not if you're actually playing or not. So you can have it in the background and have the steam time counter going off as long as SK's window is open.