According to Blizzard, Diablo III's hectic nature would make it a poor fit for the Vita's smaller screen.
Back in May, Sony told gamers that unless a "game requires specific hardware" that the company would be requiring developers to make their PS4 games compatible with remote play via the Vita. That being the case, it looks like Blizzard might be in the lucky position of being exempt from that decree. This weekend at BlizzCon, the developer confirmed that PS4 version of Diablo III, the Ultimate Evil Edition, will not support remote play, at least "not for the moment."
"The Vita is an amazing piece of kit, but the screen is still smaller," said senior level designer Matthew Berger. "And when you look at--and also it has its own aspect ratio--and when you look at Diablo III, there's a lot happening on-screen already. You get surrounded by your enemies, lots of effects flying off in every direction. The inventory can be pretty complicated to navigate sometimes when you have lots of items." A remote play-able version of the game, in turn, "would be a little bit more of a stretch."
There may still be some hope, however. While Blizzard "[doesn't] really have any plans right now" for investing in a remote play option, future plans are still "percolating in the back of [the company's] mind." While that's far from being anything solid, it's nonetheless a kernel of possibility that Vita owners can hold onto as they dream of a Diablo III they can play on their handheld.
UPDATE: Despite just recently espousing that Diablo III and remote player were no-go, Matthew Berger has now confirmed that Vita will, in fact, be able to play Diablo III, via the PS4. In a new statement Berger said that, As long as PS4 supports Remote Play, Reaper of Souls will support it." An image has also been released showing the Diablo III being played with the Vita.