I think Jeannie was less prone to breakdowns in her powers than Samantha, who often needed Dr. Bombay to break a hex or get rid of some weird spots on her face. On the other hand, Jeannie was always being ordered back into her bottle by Tony Nelson. I don't think he played his cards quite as well as sophisticates like you or I would have.
All Jeannie wanted was to be loved. Tony was a cruel, cruel master.