On March 31, Sony will be closing the PlayStation Store on PlayStation Portable in North America and Japan.
Per PlayStation Support, you’ll still have access to your Download List on PSP and content can still be purchased from the online PlayStation Store:
On March 31, 2016, the PlayStation Store for PlayStation Portable (PSP) system in the SCEA region will be closed. PSP system users will be able to purchase PSP content from the web-based PlayStation Store at store.playstation.com, and also access past purchases from the Download list on their PSP system. Users will continue to have the ability to make in-game purchases from their PSP system.
PSP’s in Europe had lost access to the PS Store back in September 2014.
Select PSP games are also available for purchase on the PlayStation Store for PlayStation Vita system users.