if they are smart, no

No.

After how quick they were to throw in the towel on the Vita, I'm gonna say no. Unless Nintendo comes out with a hybrid that makes a portable/console fusion the new standard. Then Microsoft and Sony might follow suit.

If they do and have learned anything, they'll make give it good support for the first few years until it takes off. You want to support the console when it's new, not when the console is already dead. PS4 has the same problem unfortunately with the console having only five retail exclusives until 2015.

No. They'll probably extend the life for the Vita as long as possible, even if it remains unsuccessful.

Maybe they'll do some kind of well supported smartphone hybrid in the future.

Ninty will continue on doing both. 

to the op: Sony will go a cheaper route next in the future. Sony fans will likely demand it, and they will follow.

No way, I think they already plan to ditch the Vita in a couple of years and focus on PS4, tablets and smartphone. The gaming market in the touchdevice based industry is evolving and becoming better and better so the games will continue to improve as well.

dang we need sony to make another handheld
they better because you know we cant just leave nintendo against the rising smartphones and tablets :P

There are only 2 instances where I could see them try:

1. Make a smartphone/handheld hybrid, and put more effort in it then what went into the Xperia Play.
2. Make a bumped-up-spec download only Vita, sell it for dirt cheap as a PS4 smart device.

But something that is purely a dedicated handheld system, I doubt it.

Are you 100% sure, asking you to buy two consoles for their first party seems like a big ask. A handheld of somekind designed to display equally as well on a TV screen, with all their first party at a relitively low price, seems like a smart move.