Your view of time travel is too restrictive. The timeline isn't strictly linear and unmutable. Clearly the descendants of the Defiant
's crew ceased to exist permanently. The situation didn't vacillate between existence and non-existence. New timelines can branch off, creating new histories.
Presumably, the first time Dax convinced everyone to visit the planet eventually known as Gaia, there was no settlement and no colonists, just the barrier. When they tried to leave, they were thrown back in time. Then, their descendants lived until the Defiant showed up again, this time with colonists and an Old Odo to change the course of events. They didn't pass through the barrier in the same way, so didn't go back in time.
Should the colony have persisted in this new timeline? Maybe. The mechanisms of time travel haven't always been consistent, but that could be a result of the different methods of time travel employed.