1) You can't win.
—The Laws of Thermodynamics summarized.
A series premise that allows the heroes or the villains to win minor battles along the way but prevents them from ever truly winning their overall "war" and achieving the Series Goal without ending or completely changing the series. They can't win, because then, of course, it would end the series.
On shows with premises like these, there will be episodes in which the characters make an attempt to actually resolve the premise. The frequency of such eps can range from occasional (Star Trek: Voyager, "Future's End") to frequent (Gilligan's Island, Samurai Jack, Dungeons And Dragons). Conversely, a character may briefly rise above his Genre Blindness and try to take advantage of the permanent state of failure, consequently falling right into Springtime for Hitler.
A related trope is Perpetual Poverty; the show's plot is the characters making a living doing something entertaining to audiences such as catching criminals for money (or maybe being criminals), and if they ever had a windfall they might actually choose to do something less troublesome and therefore less entertaining.
When a show's impending end is known ahead of time to the producers, they may choose to go out with a Grand Finale, in which Failure is no longer the Only Option.
Frequently results in viewers noticing writers like to Yank the Dog's Chain.
Ontological Mysteries are subject to this trope.
See also Fission Mailed.
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