Obito can't locate him, so to ensure his safety, he'll have to be intangible at all times, but Obito has a 5 minute limit on his Kamui, so after its up, Mu cuts him down, as he doesn't need to become visible to attack with his weapons, just when he uses chakra. If Obito decides to turn off Kamui once in a while to prevent himself from ever reaching his limit, Mu will sense him since when he's in the other dimension, his chakra cannot be sensed.
Or Mu uses the Fission Jutsu, becomes visible and engages Obito, lets him absorb his clone then when he's tangible (While absorbing) Mu kills him with his blades.
So sooner or later Obito dies.