I'm a bit confused. If Baba's permanent residence was in Shirdi, how could people expect him to appear in far-off places like Dahanu?

This is a wonderful question that touches upon the divine nature of Sai Baba. While it is true that Baba's physical residence was permanently in Shirdi, and he only occasionally traveled to the nearby villages of Rahata, Rui, or Nimgon, his state is described as inscrutable. As detailed in Chapter 40, Baba is a complete master of miracles, a 'Leelavatari,' who can move freely by His mere will. The concepts of "coming" and "going" are worldly and do not apply to Him in the same way. He is perfectly full, inside and out, pervading both the moving and the unmoving, much like the sky. Therefore, for Baba, there is no real "coming" or "going"; He simply manifests at will.