It really depends on the game, but to me it rather feels like the opposite, I tend to enjoy a game that I already know even more when I replay it. Maybe it is because I already know what to expect from it, and not having some unfulfilled expectations, perhaps.
Take Metroid: Other M for instance. I finished another run through it lately, it was maybe my fifth or sixth time that I finished it since I got it ten years ago. When I first played it I didn't know the story or how the game unfolds, so naturally there were expectations in my mond that sadly stayed unfulfilled. I wanted Samus to become badass but she didn't. Nowadays, I think, many people know that the game has a rather weak story. Fast forward to now and I can instead leave the story aside since I already know it and enjoy the stronger aspects of the game. That way the game certainly grew on me.
So this happens quite often to me. I really like replaying old games.
