Is there any reason why game companies can't develop contracts that allow them to keep music in a game forever?
Money, the terms would be really hard. But, also, licenses shift as companies or people who own the licenses are bought and sold, or... as is the case with so many music artists, die. No other medium other than videogames has something like ambient music "in the background" that the player can control... Like, while there's licensed music in movies, it's pretty rare for a character in a movie to "flip through the radio" and have 50 different songs play, but this is just something you come to expect in a videogame.
After GTA:SA music publishers and artists woke up to the fact that these games sell tens or hundreds of millions of copies and are billion-dollar properties long term. THis shifted Rockstar to have to go for much more niche music for GTAIV and GTAV. THey have a few hits on there of course, but most of the songs on Throwback FM or the 80s/90s rock station in GTAIV or V aren't the hits from those generations... it's like the B-sides from those generations. Even Non-Stop Pop from GTAV, I think that's an amazing playlist, but for something that is supposed to be a pop station, it's mostly like hipster Bsides of pop, Pet Shop Boys, GImme More by Britney, maybe one or two actual mega hits (Rhiana Only girl in the world), etc.
Where as ... GTA:VC and San Andreas had legit bangers. The 90s rap station in GTA:SA was literally a best of from 91-93, and then they so cleverly had the "Master Sounds" station which was tons of the original funk songs that the 90s hip hop songs used as samples. I knew about sampling from the 1990s music licensing/sampling "wars," but didjn't know any of those original songs... and I feel like playing the casino tables in Las Venturas is what introduced me to all of those, like "WTF... this is Express Yourself... isn't it........" Now, sadly, "Master Sounds" radio station in GTA:SA has lost a ton of iconic songs.
I'm sure Rockstar tried to get long licensing terms for GTAV, but I wouldn't be surprised if some of those songs start dropping off, especially the classic rock ones like Seger. Seger was notoriously anti-digital licensing for ages anyway. It was really surprising he had tracks in GTAV to begin with.
You're also seeing license disputes in TV with streaming.