Considering that the Tribunal members were able to live for several hundred years without direct contact with the Heart (House Dagoth began blocking Almsivi's access in 2E 882 and the events of the game occur in 3E 347), it would seem that elves are capable of living much longer than 200 years. I suppose you could argue that they had access to information that the majority of Dunmer didn't from their time spent as gods or that the heart still had some residual effects on them.
The Heart still had a large amount of effect on them. They didn't just loose their powers the second they could no longer get to the Heart - they faded away over a, long, long time. Arguably, the only effect of the "destruction" of the Heart seemed to be that they loose their powers
faster. Though I'm a bit tired at the moment, and I don't pay to much attention to what I'm remembering. :dance:
Anyway, faith = power in the TES universe, so as long as people still believed in them, the Tribunal would still have powers. In fact, it seems like the loss of faith in Vivec is what will cause the http://tvtropes.org/pmwiki/pmwiki.php/Main/TheEndOfTheWorldAsWeKnowIt in the end.