When the human race is forced to evacuate Earth, it leaves behind an aging, osteoporotic millionaire, who finds solace and purpose in the company of an autistic child.

After humanity has evacuated earth because of an impending radiation blast, an aging misanthrope must find solace and purpose in saving an autistic child left behind by accident.

I like Tony's version better because, among other things, the billionaire can opt out; he doesn't have to rescue himself or anyone else. But he chooses to do so even though it will cost him his fortune and perhaps his life.

Protagonists becomes heroes when they can opt out of risking their lives, their fortunes, their sacred honor-- but they choose to opt in (As Katniss Everdeen does in "The Hunger Games" and Peeta Mellark and Meg do in "The Hunger Games: Catching Fire".)

Excellent points by dpg (and others) above. Below would be my take:

'A reclusive billionaire builds a rocket to Mars to save the life of a young autistic boy, who has been left behind after Earth's evacuation due to an oncoming comet.'

In my mind, the premise raises a number of questions, some of which have been noted by others.

1] Why is there a forced evacuation?
2] Evacuate to where?
3] How does the evacuation take place?
4] How many of the 7 billion plus people on earth get to go?
5] What is the fate of all the rest?
6] How is possible that the old man is the one and only seniorized citizen to be left behind because of osteoporosis that makes him unfit for space travel? Wouldn't there be millions of seniorized men and women like him whose osteoporosis would disqualify them? (Particularly women: they are more prone to osteoporosis than men. Have you thought about making the protagonist a woman?)
7] Ditto for the autistic child; wouldn't there would be so many others like him? Why is he the ONLY one left behind?

A story can take only take so many liberties with reality and remain credible. This premise takes so many liberties, would have me suspend disbelief again, and again, and again, and again before getting to the principal plot about one old man and one autistic child.

Than you guys so much for your comments! The real emotion of the piece comes from the transformation of the osteoporotic dude (that's bone brittleness, BTW). He has been denied passage to the moon because his condition would prevent him from surviving the ascent. So he has tons of bitterness and resentment built up. In the end, he has to pilot the rocket to take the little girl up himself, which shatters his skeleton--hence the title, "Broken." So basically it's about this bitty, crotchety old jerk who has lived his life shoving all of humanity to one side, but who redeems himself in death by making the ultimate sacrifice. This logline has been a real nightmare to write, because I'm not sure how to convey all that in 30 words or less!

I would just replace millionaire by misanthrope, otherwise it's nearly perfect.
It would attract the baby boomers. Hollywood and the rest of the world are suddenly discovering that older generations have money and are more likely to go and watch in a cinema non-blockbuster movies than teenagers who will just watch it on electronic devices (iPad, iPhone, tablet ...).