Sony has announced that the PSP Store for SCEA and Japanese territories will be shuttering March 31st. Users can still download games they already bought and DLC content on their respective devices and they can still buy PSP games from store.playstation.com.
This comes in at the same time as Sony has also announced that the PSTV will also be discontinued in all territories as well, instead of just Japan.
Personally, both of these are very sad stories as I still use a PSP Go as my secondary gaming handheld, and recently bought a few games on it. I also use a PSTV nearly daily to play my PS4 on a secondary monitor.