Do any Buddhists say that everyone's Buddha nature repeats an infinite number of times?

Do any Buddhists say that everyone's Buddha nature repeats an infinite number of times? To be specific, I mean that everyone's -- including Sakyamuni's -- life, or perhaps just karma, is repeated over and over again, timelessly and forever. I'm asking, because I think that's what I believe [that's all]. The Fan Wang Ching says that Sakyamuni manifests *billions* of times, but does anything claim he appears an infinite number of times, or eternally [I don't mean permanent].