The PSN will be down while they perform routine maintenance starting tomorrow morning, Thursday, January 17th. “This maintenance will start at approximately 8:00AM PT (9:00AM MT / 10:00AM CT / 11:00 AM ET) and last until around 8:00PM PT (9:00PM MT / 10:00PM CT / 11:00PM ET). During the maintenance period, you may receive a maintenance notification when attempting to access PSN.
The PlayStation Store and Account Management will not be available during the maintenance period, but you will be able to access online play and apps provided that you have signed into PlayStation Network at some point between now and the time of the maintenance. So please be sure to sign in now if you wish to access the Network during Thursday’s maintenance window.”

So does this mean you have to sign in and stay signed in? No, you do not need to remain signed on. Just simply sign on a single time between now and the window, and you’ll be all set.