Limited Destination Time

A situation where the characters are moving from destination to destination and can't stay for more than a limited time at any particular destination or else they are stuck there. Typically this is sci-fi or fantasy and there's a piece of Applied Phlebotinum which only allows them to continue their travels during a limited time or at a particular moment. Can be a cause of Walking the Earth.

In time travel stories this can be a result of San Dimas Time, which places arbitrary limits on time travel so that the characters in the story can't simply solve all of their problems by jumping back five minutes and arranging circumstances to be more beneficial to themselves.

This differs from Flying Dutchman because the desire to continue on the journey is what forces the characters to leave. The Flying Dutchman doesn't really want to go on the journey at all.

Anime and Manga

 * Popotan: Three sisters live in a time travelling house over which they have no control, and only their Robot Maid knows when it's due to depart for another time.
 * Galaxy Express 999: The policy of the train is to stay at each planet for one day of that planet's time; this can't be changed, so passengers only have that long to be on the planet.
 * The train in FFS.
 * One Piece has the log poses, which tell you where the next island is. If you go to an island and want to go somewhere other than where the log pose will set itself to, you have to get off the island before that happens. That was the situation in Jaya: they needed to make sure they left before they lost the heading for Sky Island.

Comic Book

 * Zig Zagged by Access from the Marvel vs DC comics. His power is twofold. One is to travel between the two comic verses at will (and can take others with him). The other is that if he remains in one world too long, crossovers will begin to occur with greater frequency and volatility until the worlds merge into the Amalgam universe.

Literature

 * Inverted in Rendezvous With Rama. Rama, the eponymous Alien Artifact, is passing near Earth for a relatively short time so they have limited time to explore it before it goes away forever.
 * In Enid Blyton's Faraway Tree stories, the eponymous tree contains a portal to a magical land, but which magical land it leads to changes regularly. There's at least one story where the protagonists stay too long in the magical land de jour, and when they go back to the portal they find that it's moved on, leaving them stranded.
 * In The Secret of Platform 13, the gump is only open once every 9 years for a full day, if someone from the Island doesn't make it through the gump by the end of the day, they're stuck until it opens again; which of course happens to the prince at the beginning, starting the plot of the book

Live-Action TV

 * Stargate Universe: The ship decides on its own how long it will stop at each planet, and this is out of control of the crew.
 * At least in the first half of the series.
 * Space: 1999: The moon is hurtling through space and can only stay near a planet for a limited length of time that the inhabitants can't affect.
 * Sliders: Whenever our heroes are deposited in a new alternate universe they only have a certain amount of time (as indicated by their gizmo) before the portal can be opened to the next one. It is implied that missing the deadline leaves them stuck in whatever world they were in for 29.7 years, and if they activate the portal again too early (as they had to do in the pilot) it messes up the co-ordinates so they get sent to a random world rather than the one they came from, thus kicking off the whole premise of the series.

Real Life

 * Many fly-by space probes, most notably Voyagers 1 and 2, only had a limited time to explore their targets before their trajectory carried them out of range.