Sony's continued supporting their older consoles since the release of the PS2, when the PSX was the past console, however, it's never really hurt the company during those times. Just like the PSP compared to the Vita, the PSX compared to the PS2 is a difference in power, or the PS2 in comparison to the PS3, but at the same time, the Vita has no other portable that's as powerful as it is, where the Dreamcast, Gamecube, and Xbox were comparable to the PS2 while the 360 is comparable to the PS3. Even if the consoles didn't get as many exclusives, which we'll use the PS3 as an example, there would always be the third party support as games seemed to be more profitable on the PS3 and 360 than just releasing them on the PS2.
Even if Japanese only, there's been a lot of games that have been announced and released for the PSP lately. Not only could this the reason why the Vita lacks any games, but also be the reason why the sales of Vita in Japan are so poor. The Vita is not only having to contend to the 3DS, but also to the PSP.
I think Sony should announce that as of a certain date they're no longer going to be printing any new PSP games although will give some exceptions if developers are far along into development. Any games already released prior to this date will get printing as needed. This would force developers to move to either the Vita or 3DS. While some developers might instead choose to support the 3DS, there's a good chance that other developers would move over to the Vita. The rare game that's been mutliconsole on both the Vita and 3DS seems to have sold close to the same amount.
This would get more games for the Vita and get more of the Japanese to start investing in the Vita since there'd be no new PSP games. Also with more Japanese PSP games, there'd be more of a possibility that the Vita might get more games in the west. Very small probability since barely any Japanese games make their way outside of Japan or China, but a probability nonetheless.
I know this isn't going to happen, but who else thinks Sony should abandon the PSP. Or atleast abandon the PSP for a year or two, and maybe after a year or two allow developers to start releasing games on the system again.










