To answer your question a bit more thoroughly, there Resistance has never made any notable attempts at freeing Ala Mhigo, at this point the Ala Mhigo Resistance are too weak to do anymore than skirmishes. This is likely intended as a plot device to allow content later on for the player characters to come in and save the day by defeating the Empire and freeing city (I expect this to be in an expansion). If we won back Ala Mhigo that would be a HUGE blow to the empire as that is their biggest foothold in Eorzea and their connection between Eorzea and Garlemald.
While we can be certain there have probably been at least a free uprisings, the only one we are ever made aware of specifically is the one we take part in during 1.0.
While we can be certain there have probably been at least a free uprisings, the only one we are ever made aware of specifically is the one we take part in during 1.0.