PSV needed more support from Sony and lower launch price, as Ninty already showed that not even the market leader could ask too much and had to cut 3DS price precipitously to save it. Sadly Sony couldn't afford it back then, saving PS3 had been slow and painful and almost all the available resources had to be allocated on PS4 development to ensure it succeed. In hindsight, allocating some tens millions for two or three more 1st party games in the launch window and first year and giving Capcom what it wanted to make a Monster Hunter game for PSV could have made it far more successful (although far less than PSP, the drop of 3DS from DS can give us an idea of how much PSV could have sold, probably around 30M, maybe 40M if everything went well).

Few worthwhile exclusives.
Too expensive.
Poor 3rd party support.
Non-Gaming features were made irrelevant by smartphones.

Finally I'd like to add one thing that definitely did not kill the Vita. Smartphones being able to play games. People like to talk about how smartphones offered a cheaper ubiquitous gaming option, as if that hasn't always been a thing in the handheld market. Tiger Electronics didn't kill off the Gameboy, but somehow we blame smartphone games for killing Vita and 3DS?

Bold: Rich 3rd party games actually, but almost none of them are system seller.

2nd bold: 3ds didn't sell too big, but not a doa level like vita.

This.