PSP is making money for Sony right now, both on HW and SW it sells. And as others have pointed out, killing it now would move the customer base to the 3DS, not to Vita. It makes no sense to kill it right now. Made sense for Nintendo to kill the DS at that time, the same doesn't hold true for Sony and the PSP now.
SCEJ's reliance on 3rd party SW has finally bitten them in the ass big time. It's also pretty obvious that the PS4 is in jeopardy there with all major JP franchises going to the WiiU, seemingly exclusively (only FF and KH are missing right now, but I think they will go there do if nothing else changes). Other big but non million selling franchises such as RE has been hinted as well. Same thing happened with SCEA and SCEE at the beginning of this generation when MS literally took all 3rd party games and made them multiplatform games, often (timed) exclusive, and better on 360. SCEA and SCEE stepped their game up though and have created a plethora of franchises, some are hits, some are misses, but they were able to establish some good franchises and even some system selling ones. On top of that they are growing and the outlook there looks good. SCEJ on the other hand is diminishing and their outlook does not look good. Puppeteer and Rain look decent, but so did Patapon and Locorocco. At least they are publishing SCEA and SCEE's games now instead of letting others like Capcom publish them (Capcom published GOW games prior to 3, maybe unsurprisingly 3 sold the best in JP, by far)
SCEJ's two biggest franchise are in steep decline. GT has failed to reach 1 million sold for the first time in JP and HSG can be considered a 200K IP now. Honestly, Soul Sacrifice should have been made for the PSP around MH3 time. Legend of Dragoon and Dark Cloud should have gotten a remake or sequel 3 years ago. New RPG IPs should have been created, they did well by going to L5 during the PS2 days, but L5 is doing its own thing now and WKC was horrible probably because L5 was focusing on other things at the time and just wanted the paycheck at the end of the day. Given that they can't even update the xmb/browser and won't let SCEA/SCEE help with it, I do not feel confident they can turn the situation around. Heck, the new store only came to fruition because SCEE was able to pull that away from SCEJ's dirty claws. Outside of buying a big 3rd party partner, I think the future of playstation in Japan is pretty dim.