Worth noting that the current Vita sales are due to Sony's many fuckups in its lifetime (same with Wii U). Poor control scheme, overpriced internals, terrible razor-and-blades monetization model, bad market positioning, you name it, they did it.
That said, even if Sony were to cut every reasonably available corner and put out the near-mythical $149 device (with a modicum of software support, no less and preferably somewhat better than current), it still would not reach more than - optimistically - 30 million lifetime sales (probably double the Vita's would be a more grounded estimate).
However, device sales alone are only part of the picture.
It has been repeatedly stated, in various semi-official communiques, that the Vita has the second highest attach rate of any gaming platform ever (first evidently being PC). According to several back-of-the-envelope calculations, the median attach rate for the device -- excluding the lowest 10% (who bought about 3-4 games then dumped it) and the highest 10% (with 100+ title libraries) -- rests somewhere in the vicinity of 15 titles. While a considerable percentage were acquired during sales, clearances, PS+ giveaways et al, money did change hands. The monetization rate is sufficient for Sony to keep it on their books and for indie devs to produce Vita versions (admittedly, with some measure of Sony support).
Would a newer, cheaper device that can still play those games at good performance find a niche in today's market? Likely yes. Would Sony have enough courage to go for it? Unknown. Today's Sony is a rather risk-averse company. The lure of high software sales (compared to the inevitably middling hardware ones) might not be enough.