When the patron god is sent to heaven, his dependents keep their falnas, but they will be blocked so for practical purposes it is as if they did not have it. To reactivate it they must receive the falna of another god and it will be exactly the same as they had previously, that is, it will not restart.
The case of Finn (Dim) and Fianna is different, their source of power was not the falna since gods had not descended to the nether world at that time. Their source of power was due to an ability of their souls called BloodFury Spear that in effect made them as powerful as first-class adventurers.