When you mention innovation, I think of Detroit and its depopulation. Last year it lost its place as one of the largest 20 cities in the US: http://www.detroitnews.com/story/news/local/detroit-city/2016/05/19/detroit-population-rank-lowest-since/84574198/
That story does not go deep into the reasons why it has lost over half of its population in a few decades, but it might have something to do with the stagnation of the heavy manufacturing business on the one side and precisely innovation -in the form of automation- in key industries like the automotive one.
Cities are not necessarily inmortal, but there are some that are definitely long lived. I believe current Baghdad lies a few miles from Babylon, Jerusalem has been there for most of recorded history, as well as Constantinople/Istambul, to name just a few. It might be related to advantageous location-more people coming-everything gets increasingly more organized around said advantageous location-we forget how to do things away from it.
But cities do die. Sumer died. Teotihuacan died. Chichen Itza died (but I am based in Mexico City and the Great Tenochtitlan thrives).