on this page
http://wiki.spiralknights.com/Arcade
it says
The gates themselves rotate like the rest of the Clockworks and are shifted along every two days (as there are four active gate slots, each gate remains accessible for eight days).
I thought it was every day and a half, or 36 hours.
It definitely used to be 48 hours. Gates would rotate at 20:00 game time every two days.
I haven't checked since the four dormant gates were removed.