Hard to say. Winning decisively with the PS4 after the comeback-kid story of the PS3 is definitely great for the brand but losing and abandoning handhelds is rough. I have a PSP and I love it. It's my N1 handheld of all time. I wanted more of that type of experience separate from what the DS/3DS did but obviously I'm in the minority.
It makes me wonder if Sony is going to try at a hybrid system like the Switch at some point. People here in this forum and elsewhere accuse Sony of being a copycat of Nintendo and even as fan I can sort of agree with the point. That being said, even if you took someone else's idea, as long as the execution is good and they bring the games then they could definitely succeed and redeem themselves after the Vita debacle.