Unfortunately, we still don't know when it will return.
The PSN has been partially restored, but online play is only one of the services offered by the PSN. The PlayStation Store is still down, and while we don't have a return date, we do know how Sony plans to deal with the backlog of games that weren't released while the network was down. Even though the PlayStation Store traditionally updates every Tuesday, Sony will introduce multiple updates each week until the store is caught up with all the content that was shelved as a result of the outage.
"To date, three Tuesday publishes were missed, which included items like Under Siege and the MotorStorm Apocalypse demo," reads Sony's latest FAQ. "Rest assured that you won’t miss any of this great content. To catch up on the large amount of material, we’ll be publishing to the PlayStation Store multiple times per week once commerce functionality is restored. We will update the PlayStation.Blog with information on timing of the Store restoration, as well as the full list of new content as each publish occurs."
While it's good to know that Sony will be releasing the missing content as quickly as possible, game developers are getting the short end of the straw since titles that would have normally received a full week’s worth of promotion are now going to have a much shorter window in the spotlight before they get pushed aside to make way for other games that were also supposed to be released. I guess it's better to share the spotlight than to get no spotlight, but that's probably not enough to make up for the lost time on the Store.