We have dual zone and for some reason, the upstairs fan stopped running when we flip the switch from "auto" to "fan". We were given the advice that if you turn on the a/c downstairs, you should turn on the fan upstairs but not the a/c, only the fan in order to circulate the cold air from downstairs to help save energy. Why do you think the fan stopped working? We've been doing this exercise since we moved in late March when the temperature is above 90 degrees. Any input is appreciated.

Dual zone or 2 systems? Dual zone would indicate 1 system with 2 zone valves. Sounds like you have 2 separate systems and what you are doing won't work that way as cold air will not flow UP and the systems are not connected. Thermostat could be bad.