Slim to none chance of a Sony handheld console ever replacing the Vita. And with the market situation for the PSV, it's hard to say if manufacture will even continue for 18 months from now. Support is probable to some degree or another through fall 2016.
It's weird to say, but a PS-branded Xperia mobile add-on is more likely than another dedicated handheld console, because it would be an absolute fraction of the cost of developing new specific hardware. Tacking on a controller/buttons to a kit that attaches to Xperia phones, along with porting IPs/games to it in more limited fashion would be an interesting concept (doomed to fail if done poorly, but could succeed if they hit all cylinders properly). I think if the kit was basically universal for qualifying android phones AND had truly amazing games/IPs it could be a hit, but come on now, the odds are still slim as hell.
The smart money by far is Sony simply abandoning mobile gaming by and large, but probably licensing IPs for mediocre touch-screen gaming for iOS/Android. You know, the usual blah quality, $4.99-$14.99 forgettable shovelware that constantly pushes past the app stores.
It's sad, because the PSP was the most successful non-Nintendo handheld of all time, by a pretty huge margin, but the Vita fell right on its ass. It's not even a certainty by any stretch that we see a full Nintendo replacement for the 3DS, although that is considerably more likely to happen in contrast.