1. Poor naming. It broke the PS naming convention and confused consumers. Most people don't know what a Vita even is. The PSP2 would have sold phenomenally better.
2. Too little advertising. The Vita has the most remarkable lack of advertising I've seen. Given the unwise, artsy name, it would have needed a lot of ads to raise public awareness. Xbox One is a stupid name, but MS's ungodly ad budget makes up for its inherent awareness deficit.
3. The wrong kind of advertising. PSP ads helped to sell an awesome gaming machine by also showing off its then-remarkable multimedia features. Sony tried the same with the Vita, but smartphones had made this emphasis a null point. Thus, it didn't look like something people "needed."
4. Handheld decline. The Vita is doing horribly compared to the PSP, but the 3DS is doing horribly compared to the DS. This gen has seen a massive handheld decline, most likely attributable to smartphones and tablets. The market itself is much smaller, and this actually accounts for a surprising amount of the PSP-Vita decline.
5. Digital focus. The Vita has/had too strong a digital push, resulting in limited shelf space and lack of awareness of its games. The expensive memory cards only make it worse.
6. Inconsistent messaging. Once the Vita had all of the problems, Sony did not develop a coherent strategy to rebrand the Vita the way Nintendo did with the initially failing 3DS. Indie machine? Niche Japanese gaming? Remote Play hub? Multimedia device? Console games on the go? The truth is that it is an amazing nachine -- all of these things and more. Alas, this creates a confusing identity for the system and results in hyperbole by internet halfwits claiming that the system is "abandoned," which is clearly untrue to a hilarious degree. However, that affects other uninformed people and creates a common myth that works against the system while it continues to receive and abundance of titles and features.
EDIT:
To address your last questions, I'll offer this synopsis: The Vita was doomed to an extent from the beginning due to handheld decline and poor market positioning in the rise of smartphones. However, it could have done better than it has with a smarter name, more advertising, and a tighter PR message to sell people on what the device is supposed to be. I find the Vita incredibly easy to recommend to people and always find them very happy with the purchase. Sony could have done the same.
Mind, the Vita continues to receive phenomenal games support and has the most "core" audience of any system, meaning that Vita owners buy more games per person than what we see on any other platform. Furthermore, it continues to sell steadily and even sell out of its low production capacity at times. The Vita is not abandoned and is not a failure; it is a vital component of Sony's goal of creating a vibrant PlayStation ecosystem. However, it is also not what it could be.
