Imagine a market "Aliens will be found in the next year" where when you buy shares they dynamically adjust due date.

So it would be a permanent market but shares would expire individually. One problem is that shares wouldn't be easily tradeable.

I think for many markets this may seem more natural than how we currently pick a random date in the future and then bet yes/no on that.

Other examples: I'd like to make markets about my city like "will X store go out of business in the next month". In the current system there's no way to make that into a long term market. But with continuous markets it could go on for years with everyone on the same market page.