Rand Simberg ties papal succession (a topic I have to admit I didn't see showing up here) and healthy life extension together in his latest article:

Despite his years, though, they may get a lot more continuity than they bargained for. This is, after all, the twenty-first century, in which technological breakthroughs in general, and medical breakthroughs in particular, are coming along at a breakneck and accelerating pace. Such advances, described in the recent books More Than Human by Ramez Naam, and Joel Garreau's Radical Evolution, may upend (among many other things) the stately applecart of traditional papal successions if (as seems increasingly likely) they result in extreme life extension and indefinitely-long healthy human life spans.

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In a world of conventional life spans, we can always console ourselves with the thought that, if we're stuck with a dud pope, or a particularly nasty and competent dictator, or an overactivist judge, no one lasts forever.

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If, as many think, this pope was selected to provide at least a temporary bulwark against modernity, how ironic that one of the features of modern life that he might be having to fight could also be one that could allow his own obstruction to it to be permanent

I think that it's clear that change means change - as and when scientists attain funding enough to build the technologies of radical life extension we will start to see shifts in society to match. I imagine that lifetime positions will be one of the first to go. Large organizations like to maintain the status quo, and the status quo is a certain amount of turnover.

As a side note, I've never found the immortal dictator to be a particularly convincing objection to healthy life extension. For a start, it's also an objection to all modern medicine and its life-prolonging effects. Secondly, how many dictators manage to maintain their position for life at the moment?