The one relationship that immediately springs to mind, when I think of this type of thing, is Elton John and Bernie Taupin.
I understand that they split up for a while, and that Elton John's music lost its lustre during that period.
Although I like some of Elton John's work, I am not enough of a fan to speak in more than a fairly vague sense. I just remember people complaining about it, when it was happening.
Keith Reid was also given top billing, for Procol Harum. He usually showed up in group photos.