the pace of change of our subject matter here is much slower
This is true, but it is not zero. We don't have to keep pace with Stack Overflow to be a useful site. If nothing else, the rate at which language changes provides an ever moving target for theology to express itself. This has always kept Christianity on its toesThis has always kept Christianity on its toes. I see a continuing use for this site that reflects that.
[...] is there a danger we may reach saturation point - when there are no "good" questions left to ask?
Yes. There is a saturation point, but I would suggest that it is far far beyond our current scope. With several thousand years of history and miscellaneous doctrine and practice to delve into, I don't think we will be reaching saturation point any time soon.
It is likely that a smaller and smaller percentage of what people think to ask off the top of their heads will not have already been asked. However with the wide range of permutations that can be examined, I don't expect the well of possible questions to run actually dry in my lifetime or yours.
Is C.SE sustainable in the long term?
Time will tell. My bets are on yes.