It's not a matter of browsers, as it first seemed...
The session table (which stores who's online and logged in) was full. Sessions tend to vary in length depending on how forums are set up, we have 4 hours. The table is usually cleaned on an hourly basis, which together with the timeout and the amount of concurrent users we have seems to work well generally. But if too many users are using the site simultaneously, the table becomes full before the maintenance tasks clear out the ones that timed out, and thus refuses new sessions (say, logging in on another browser).
At least, this is my understanding of the issue.
Some forums have far lower timeout length; some in the range of 15 minutes, to avoid these things, but it's a real drag to have to come back to your tabs and have session expired... I might lower it to 3h or even 2h though, 4 seems a bit excessive.
It is expected to occur occasionally under heavy traffic; it resolves itself in time. Unless there is a sustained high traffic, due to regular use or deliberate DoS attacks.
In the morning I cleaned up some spam; that might (or might not) have added to the usual load. Also, holidays are near, there's always increase in traffic in the holidays...
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