The Great Repair

Freedom: seven letters that can start an avalanche of impassioned speeches and any number of revolutions. Also, something that characters and players are frequently deprived of in fiction. A frequent plot element used in stories is to trap the characters in an inescapable location. Well, mostly inescapable. The only means of escape is a damaged car, plane, ship, space ship, Time Machine or weirder vehicle. In order to escape this Closed Circle they have to repair the vehicle, which won't be easy (otherwise, what would they do for the rest of the episode?). Usually this will require a chain of Fetch Quests for tools, parts, fuel, and potentially crew members.

If the vessel is large enough, they may well be trapped inside it and adrift at sea / space / Hyperspace / the time stream, often with the further inconvenience of dwindling supplies and leaks. For extra fun, there are enemies inside and outside the vehicle intent on killing them, and wherever it is they're trapped is about to get attacked and/or destroyed, so there's a time limit on escape as well.

Named after the film The Great Escape, where Allied POWs plan to escape their prison.

Examples of The Great Repair include:

Film

This is the main plot of Apollo 13.
The Flight of the Phoenix: After their plane crashes in the desert, the survivors build a smaller working plane (little more than a flying wing) out the remains of their crashed aeroplane.
In Titan A.E., after being stranded on a "drifter colony" made of the fused-together hulks of old spaceships, Cale gets the idea that one of the dead ships might be fixable. He and Akima set about repairing and restoring it in order to use it as transportation.
Pitch Black. The survivors of a starship crash on a remote moon must move power cells to the skiff (a small starship) so they can refuel it and escape.
Christopher's entire goal over the 20 odd years that has passed in District 9 is to get enough fuel to escape Earth and return home to get help.
This makes up a fair bit of the plot of The Empire Strikes Back on board the Millennium Falcon

Literature

The Vorkosigan Saga prequel Falling Free has elements of this. The plot requires the characters to gain control of a space station, jury-rig it into something moveable, and then hijack an interstellar cargo vessel in order to escape. So technically they're building new stuff, but it keeps breaking while they build it...
Robert Heinlein's Space Cadet. After their ship sinks into the mud of Venus, the cadets must repair an old damaged ship, the PRS Astarte, in order to escape.

Live Action TV

This is the plot of the Firefly episode Out of Gas.
Averted in Gilligan's Island: The Professor immediately declares the Minnow unfixable... and then goes on to build an entire village out of bamboo, not to mention various forms of implausible technology.
In the final episode of Lost, the remaining survivors escape the island by repairing the Ajira Airways plane that crashed there over a season earlier.
The Six Million Dollar Man episode "Little Orphan Airplane". Steve must repair an airplane that is his and his companions' only means of escape from a dangerous warlord.
The Star Trek: The Original Series episode "The Galileo Seven". An Enterprise shuttle crashes on an unknown planet. The crew is repeatedly attacked by primitive humanoids and there's dissent amongst the crew over Commander Spock's decisions. They eventually escapes after Scotty repairs the shuttle.
Subverted in The X-Files episode "Dod Kalm", where Mulder, Scully, and a couple of sailors are trapped on a derelict ship, try to get it to work again, but fail and have to wait for extraction. Mulder and Scully are the only ones to make it.
Doctor Who: In the episode "42", the Doctor and his companion are trapped on a damaged spacecraft which is falling into a sun. They are separated from the TARDIS by the rising temperatures and must repair the spacecraft to escape.
- In the episode "Voyage of the Damned", the Doctor is trapped on board a space replica of the Titanic in orbit around Earth, and must get it flying again to keep it from crashing into Buckingham Palace.
- In "Planet of the Dead", the Doctor must improvise repairs to a city bus, severely damaged in a wormhole trip to a desert planet, in order to drive it back through the wormhole to Earth.

Tabletop RPG

Classic Traveller Adventure 3 Twilight's Peak. In the Backstory, several starships crash landed on a deserted planet. Using parts taken from the others, the crews repaired one of the ships well enough to escape.
In the Crapsack World that is Warhammer 40,000, the account of Fulgrim performing The Great Repair on the planet of Chemos made it such a beautiful shining beacon in the midst of darkness. Dropped in a dying planet where resources are strained, he resolved to fix it all. Reclaiming old resource plants, increasing efficiency and eventually rebuilding the entire Chemos civilization, he turned a dying planet into such a beautiful splendor in mere 50 years. An unambiguously happy ending for the people of Chemos. Unfortunately, one ending is often a mere beginning to another story...

Video Games

In Dead Space, repairing the Ishimura and finding out what the hell happened to everyone on the Zombie-infested station are actually secondary priorities to surviving.
Oo-Topos (1981, 1987). Your ship has been forced to crash land on an alien planet. You must escape your captors and repair your ship so you can escape.
Pikmin revolves around finding the missing parts for your damaged spaceship after crash landing on a strange planet. What ending you get is dependent on how many parts you can salvage before your life-support gives out at the end of its 30-day limit.
The Scott Adams game Strange Odyssey required the player to find equipment and repair his spaceship to escape a tiny asteroid.
In Commander Keen Episode I: Marooned on Mars, Keen must find the necessary parts to repair his Bean-with-Bacon Megarocket so he can return to Earth.
The first Toejam and Earl game has the titular aliens crash-land on Earth, where they have to find all 10 pieces of their spaceship so that they can go home.

You should never let Earl drive.

In Fallout 3, after the Brotherhood of Steel's giant stompy robot Liberty Prime gets trashed by an orbital bombardment, Scribe Rothschild swears to rebuild it no matter how many years it takes.
In the Atari 2600 E.T. game, the alien must assemble a communications device to summon a spaceship, by finding pieces scattered around the game map.
This is key to the plot of Subnautica right from the first minutes of play -- your Escape Pod was damaged during your crash landing, and fixing its broken subsystems is key to progressing further in the game. Repairs are a key part of surviving in Subnautica, including repairs to the crashed ship to keep it from dumping radiation into the sea you have to live in. Averted in the end game; while you have to assemble an escape rocket, you actually build it entirely from scratch rather than gather its broken parts and fix them.