In Quidditch the game only ends when the Snitch is caught, but what happens if the Seeker can't catch it? The house in the lead would win, wouldn't they? Where do the teachers draw the line to the end of the game?
The game can also end by mutual consent of the team captains:
A game of Quidditch ends only when the Golden Snitch has been caught, or by mutual consent of the two team Captains.
Quidditch Through the Ages - page 28 - Scholastic - Chapter Six, Changes in Quidditch Since the Fourteenth Century
Previous answer has a quote for Quidditch through the Ages so those might be the rules. But I find it hard to believe that option was used very often :)
In HP1 Wood explains:
"A game of Quidditch only ends when the Snitch is caught, so it can go on for ages -- I think the record is three months, they had to keep bringing on substitutes so the players could get some sleep." - HP1 Chp10
That seems in tone with the "Atmosphere" of the world. It's preposterous to continue playing for ever so I'll bet that just what they'll do!!!