Shigenori Yoshida, a spokesperson for Sony in Japan, told Bloomberg today that the company plans to have the PlayStation Network and Qriocity services fully restarted by May 31.
This will put the outage at a total of 41 days -- over a month -- by the time it comes back up again. But it's likely a conservative estimate by Sony, and the company is also planning on bringing back functionality in stages. According to a forum post on the European PlayStation site, "restoration of Online Gamplay [sic] is the FIRST phase of the plan to restore the PSN."
This means that with any luck, online gameplay functionality will be back very soon, with functionality such as the PlayStation Store, Qriocity and other online services restored by the end of the month.
It'll certainly be interesting to see if the PSN outage affects the sales of upcoming multiplayer-centric titles such as Brink.