According to Sony's president Yoshida, when asked if the Vita would ever have a successor, "the climate is not healthy for now because of the huge dominance of mobile gaming." This means we likely won't be seeing another handheld from Sony, at least not in the near future.
This honestly isn't surprising to me in the least. PSP was only successful in the early years until DS Lite released and the DS in general finally took off, and Vita is quite obviously not doing well anywhere outside of Japan. (in fact I think it's been completely discontinued in most areas in NA and Europe) It wouldn't make much financial sense to release another handheld, and the PS4 is of course doing well, it would only take away from that.
This honestly isn't surprising to me in the least. PSP was only successful in the early years until DS Lite released and the DS in general finally took off, and Vita is quite obviously not doing well anywhere outside of Japan. (in fact I think it's been completely discontinued in most areas in NA and Europe) It wouldn't make much financial sense to release another handheld, and the PS4 is of course doing well, it would only take away from that.