If you accept the theory of reincarnation, then you believe people have many lives. But how many, and until when? In other words, does it ever stop?
In principle, the number of times you can return to Earth is not infinite, but depends on your ability to learn from past mistakes, and improve yourself until you attain what is called Nirvana, Samadhi, the Body of Light, etc. In short, a state of absolute perfection, where you’re free of all human conditioning. When you attain this level, you don’t need to reincarnate and come back to Earth… unless you voluntarily choose to do so out of compassion for other people. Some saints and great spiritual masters choose this path and return to Earth to help their fellow humans on the road to perfection.