I fly out of SFO every week anywhere between 8 and 11am. I've never seen it closed during these times, though I can vaguely recall a very early (6am departure) when it was not open.

This past Monday the priority line was open when I got there at 6:30am, but only one of the two main "stations" open (one of the metal detectors had a big blue "TSA Authorized" sign across it announcing that the TSA did not have that one in service. My tax dollars at work...). Sometimes it's just plain faster to go through the main UA domestic security line or the one off to the right (I think) of the 1K/1P check in desks.