That's entirely up to you. I don't see the IP address (the 209.157... part) changing, so it should be no harm in keeping yourself logged in.
As a side note, if you didn't log out the last time you were able to use freerepublic.com as the address, once it comes back up, you should still be logged in.
Also, not sure if this is all that important, but a Google search on "Free Republic is down" turned up some nonsense threads speculating on reasons for the problems with DNS, etc.
Unfortunately at this moment I'm on a computer with firewalls blocking my ability to respond to the disinformation on those ridiculous threads.
Kent, I have pinged you because one of the threads is from a Seattle based newsgroup. Perhaps you could shine some light for those who seem to be wallowing in ignorance on a few of those threads. Then again - why waste the keystrokes.