I've heard of reincarnation into a new life but never living the same life over and over again.
It's the old metaphysical wisdom from the stoic's, the universe is eternal in time but limited in matter and must necessarily recycycle itself. It has to be that way or the universe had already finished itself long time ago or it would be dependent on an external God or creator.
When the totallity is eternal all the parts and sequences must be eternal also, so when you dies and it takes - let's say 1001 Bazillion years to get reborn it will feel like less than a fraction of a second from the very moment when your brain activities stops.
Why? There will ofcourse be no sense of time when you are dead so no matter how long time it takes in earth years you will not feel the time passing. So you die and in a fraction of felt time you are born again and so over and over.
This IS your eternal life, enjoy...;-)