This depends on personal belief,and is different for everyone.
I personally believe we are reincarnated until we reach enlightenment,which is becoming harder in this society.I also believe that you are a little more enlightened as each life goes by.
Again,it all depends on what you think is true.
Like many people say, we all have our own opinions and beliefs. I am wiccan so i believe that i recarnate into a new life when i die to become one with the goddess, I also believe that sometimes if you dont want to recarnate you can be a helper or you finish recarnation and become one with the goddess. Anyways i dont think there is a faster way to speed up your process. Hopefully this helped, its my opinion though!
It really does rely on one's personal belief. But I believe that everyone is reincarnated until they have lived their life perfectly with the circumstances they are given. There are few who are lucky enough to remember their past lives with little to no effort at all(: