Sole Survivor (1970)
https://en.wikipedia.org/wiki/Lady_Be_Good_(aircraft)

It is blowing your mind what a man can do with the right abilities in a bad situation, like this man you are reffering into. Imagine if that blonde nerd with the glasses wouldn't aboard to the plane, what would have happened to the rest of the cast
I'm not rich!I'm just a poor man with money. (from the movie: Love in the Time of Cholera)

A French and his Citroen 2CV stranded in the 70ies in the desert after the suspension had collapsed. 12 days later, he drove out of the desert with a makeshift motorcycle, he built out of his 2CV. Pictures:
http://www.welikethat.de/2012/05/24/ein-franzose-baut-in-der-wuste-sein-kaputtes-auto-in-ein-motorrad-um/

A jet crashlanding will do so with about twice the speed of a propeller plane. That's four times the energy per mass unit, doing that much more damage.
Also, even if the crew would be able to repair the damage sufficiently to fly it away from the crashsite, turbines are usually started by driving compressed air into the engine, which is usually provided by a starter cart. (Watch the video to "Dreams" by Van Halen, there is a short scene of a ground crewman removing the starter air hose) Where would that come from?
I did not save the boy, God did. I only CARRIED him.

Something that I noticed is that all these cases of planes being crash-landed & repaired in the field involve piston-engined planes. You never see that being done to a jet (turboprop, maybe), probably because:
Jet aircraft are heavier,
They have narrower, high pressure tires that would sink in a bare-base location,
They have higher fuel consumption, so they wouldn't have much fuel to take off with,
They would need a longer runway to take off from,
And, they are much less forgiving of FOD (foreign object damage)

The closest I can think of, off the top of my head, is set during the opening days of WWII. A DC-3 was stranded in the Pacific, with one wing badly damaged. It was apparently replaced with a wing from a DC-2, and then flown away successfully. The hybrid aircraft was even jokingly referred to as a "DC-2 1/2."

I'm sure there have been instances of small aircraft with mechanical trouble landing somewhere deserted, and the pilot or someone onboard repairing it and taking off again, but that won't make headlines. But as far as the scenario in the film, it's fictional, but the whole background is factual (author Elliston Trevor wrote it).
For who would bear the whips and scorns of Hollywood (;-p)