Looking back at the PSP, we see a handheld console that had immense success around the world and at times was the most successful game system overall. The PS Vita is the successor to the PSP and it has not seen nearly as many sales, with some people claiming that the Vita is dead. The Vita's sales are unlikely to ever turn around, but the handheld console isn't dead, it's just unable to become popular due to its own issues and the existence of the Nintendo 3DS.
For the past few years, we have heard the Vita is failing and most of those claims have been accurate. Sony is not going to get rid of the system anytime soon--if anything, it has become more determined to boost sales--but sales reports do show the Vita is not popular.
Many gamers have been pushed towards the 3DS and away from the Vita due to the former's very strong game library. This year will bring some big games to the Vita but the 3DS continues to have a stronger library. A lack of good games in 2014 combined with the Vita barely being talked about during last year's biggest gaming events verified that Sony's handheld console is struggling. Yet, Sony doesn't want to give up on the device, it just doesn't have much worth saying about it.
When asked about the Vita's no-show at Gamescom last year by Eurogamer, Sony Worldwide Studios president Shuhei Yoshida summed up the state of the Vita:
We are pretty happy with games coming out on PS Vita and the games that are in the pipeline. PS Vita gamers are pretty core, dedicated gamers. They seek information, so we trust them to find out about the games coming out on PS Vita. - Yoshida
Essentially, the Vita only has a small, dedicated set of users and while Sony is "happy" with the games coming out for the system, they aren't that impressive and Sony doesn't even feel like mentioning them. Instead, that small set of dedicated Vita gamers will find out about new games on their own.
The 3DS is a whole different story. It'd be difficult to say the Vita is failing because of the 3DS, but it is clear the 3DS has been successful and there are some gamers who've picked the 3DS instead of the Vita.
Handheld gaming with the 3DS is entirely driven by Mario, Zelda, and Pokemon, franchises that have continued to see massive success and Nintendo has reaped the benefits of that success. On the Vita's side, you'll struggle to find many big game successes outside of titles like Tearaway and Final Fantasy X HD.
It wasn't always the case that the Nintendo 3DS seemed like it was going to dominate in the gaming industry, but over the years, it has proven that Animal Crossing, Pokemon X and Y, Super Smash Bros, and Pokemon Omega Ruby truly can drive millions of hardware sales.
If we go by the adage that software drives hardware sales, the Vita is never going to be legitimately successful unless some massive game comes along to drive sales. The handheld console saw tens of thousands of sales in Japan due to Final Fantasy X HD, but big game releases like that only come along once or twice a year for the Vita. When they do come along, they also aren't as big as the releases on the 3DS.
So, can we say the 3DS is the reason the Vita continues to fail? No.
It is clear however that the Vita is not going to take off and that is because the 3DS does exactly what a handheld game system needs to and the Vita does not.
Sony has created more of a handheld version of its consoles than a legitimately different standalone system. The 3DS does well standing by itself while the infrequent successes of the Vita are partially tied to regular consoles due to features like Remote Play which was responsible for a Vita sales boost.
The PS Vita is not in a position to be a big player in the gaming industry and after three years on the market, it's safe to say it may never be.