I guess it will all depend on the wording of the contracts and things like that.
With something like Olympia, I'd have thought the contract would be for bringing the coaster for 5 (or however many) events, with an expectation of annual events. But obviously if an event doesn't run in a specified year, then the ride can't be bought to the event, so it wouldn't count.
With the parks, their contracts would count years/seasons, and since the attraction is in situ all the time, it would be different. ie, the contract would be for the ride to be in situ for 5 years, not necessarily for it to run 5 years. This is where the wording and fine print of the contracts would come into play. Could an IP specify they want an attraction to run a minimum number of days in a season? Would Merlin agree to that? Does the IP still get paid if an attraction doesn't open? To what extent does having an attraction closed affect the brand name of an IP (I'd suspect it's minimal, but who knows)? All of these things could be different for different IPs too.
I remember when Saw first opened that there were rumours floating around that Lionsgate had stated that if less than 90% of the special effects were working, the ride had to be closed until they were fixed. I believe it was absolute rubbish, but many people believed it.
Personally, I'd expect the set up to be pretty basic at its heart. Thorpe/Merlin pay a fixed amount each year, and the IP get a certain percentage of the profit of merchandise related to that IP too. That would last x amount of years, and then discussions would reopen. Obviously there'd be other stuff, but that'd be the heart of it. I could be way off of course, but just what seems sensible.
At this point, with Ghost Train, I'd've thought that Derren would rather not have it run a year beyond the original planned contract ending, and just cut ties with it. It certainly feels like he's no longer connected with the project.