Vita didn't have numerous chances at anything because the price was always too high. It had zero chance of getting out of the situation it was in at that price save for a game on the scale of a mainline FF releasing for it.
If that's the case then Sony unequivocally failed to make the correct hardware design decisions from the start. If it had to be under 20,000 yen in order to move systems, they should have designed a system suitable for that price from the start and paid enough money to Square to have FFXHD released more quickly and secured, at least, timed-exclusivity for Vita. Their hubris in sticking with the 'tech over economy' philosophy was just as poisonous as Nintendo's when they originally priced the 3DS at 25,000 yen based on hype for games that were 1-3 years away from release.
EDIT: To put it bluntly, say the Vita magically sells at a base line of 30K, that's still 20 more weeks to reach 2M LTD, which puts us in August. At which point 3DS has Monster Hunter 4, Mario & Luigi 4, Donkey Kong Returns 3D, Shin Megami Tensei IV, Disney Magic Castle, Friend Collection, and a Pokemon game in two months. Even low-balling the 3DS a little at 50K per week, it'd still be close to 12 million units in the same period.