When a programme on iPlayer says "available for over a year", it always gives a date on Sky, so are never actually available indefinitely. The longest date I've ever seen recently is 2038.
There's a technical reason for that, the basic principle is explained here, though this is talking about 64-bit iPhones, the same concept of numbers wrapping round still applies:
In other words, this GIF from Wiki shows what will happen in 2038 as far as Sky and other boxes are concerned:
And for completeness, here's a BBC.com article on it and other number issues.
DE88 and Stuart gave kudos