In a message to PlayStation Network developers, Sony has stated that the PlayStation Store, barring any further problems, will be brought back up on the 24th of May.
The note came from Jack Osorno, who's the PSN content manager, as he was addressing the developers. The first release will put live the content originally planned for the 26th of April, and a few days later the same will occur for the week after. This will continue until Sony are caught up with the backlog.
Many games, such as Mortal Kombat, have been suffering from a lack of online play due to the PlayStation Store being down.