Sburb, the Reality Warper computer game from Homestuck, can be rendered unwinnable by a whole host of outside events.
Any behavior that deviates from the Paradox Space-determined Alpha Timeline will create a doomed and unwinnable offshoot timeline. The only thing that can be salvaged is information passed to the Alpha Timeline such as Davesprite's knowledge about the trap Terezi laid for John.
The destined player chain must be completed for the session to be winnable. This can go wrong in several ways: Loss of the original game discs requires finding replacements. Dave has to strife his older brother for the only extra copy, then use a game hack to replace John's lost server disc. Entry must be achieved before the meteor timer runs out. In the offshoot timeline Davesprite came from, John died fighting his Denizentoo early in the game. Without him, Jade was unable to enter the Medium and (presumably) died when the meteor struck her house. Dave and Rose can't progress past a certain point without their co-players, and Dave is forced to travel back in time to Set Right What Once Went Wrong. A player dies before entry without a backup dream self. Dream-selves salvage the post-Scratch troll session after Aradia and Sollux's deaths, and the post-Scratch human session after Roxy and Dirk's deaths.
The sprite prototyping process can break the game if not done with extreme care. First, pre-entry prototyping must be completed by all players for the Battlefield to reach the correct end-game form. The post-Scratch humans are all prevented from prototyping until after entry, resulting in a Void Game that is unwinnable without external intervention. Second, the item used for prototyping is vitally important as the game's villains gain powers and traits based on it. The pre-Scratch humans accidentally prototyped Becquerel and gave their enemies godlike powers that broke the game so badly one of the bosses escaped their session and screwed over the trolls. In the post-Scratch troll session, the Black Queen took Aradia's frog prototyping as a personal insult.
In the Game Within A Show from Scooby-Doo And The Cyber Chase, the gang is trapped in a video game, where they must find and pick up a hidden box of Scooby Snacks on each level to advance to the next. In the dinosaur-jungle level, Scooby is picked up by the trapped baby pterosaur he just rescued, and grabs up the box of Snacks an instant before it flies away with him, preventing the box from being destroyed by molten lava. As a player of the actual game might not spot the box in time, this looks like an Unwinnable by Mistake that would need fixing. Justified, as it's evidently a Beta-test version that they're caught in.
This CAPTCHA◊, and others, apparently. Fortunately, it's only actually testing one word, the other being from a large-scale project of using the whole show as an OCR (normally, it's not this obvious). One can bypass a non-typeable word by simply writing "fff" (or, depending on your vocabulary and maturity level, the filthiest, dirtiest profanity you can imagine) in its place.