The mind is finite. Therefore there exists some finite number of possible states of mind – a large number, surely, but definitely not infinite.
That being the case, and taking a deterministic view, there will be some number of series of states of mind that entail closed loops of various sizes. So imagine a certain state of mind that inevitably leads back to itself in a fairly short amount of time – i.e., within a single human lifetime. Is it possible someone has ever experienced this? Entering a state of mind that, after some amount of time, repeats. Is this what the mental experience of "deja vu" is?
Is a true repetition impossible, due to outside inputs? What if the person were in some kind of sensory deprivation tank? What of people who are "locked in" due to various neurological conditions? Perhaps in that kind of situation, what if it turned out that the mind looped fairly regularly?
[daily log: walking, 6.5km]