Didn't we have pretty much this exact same thread very recently?
Anyway, the Ottoman Empire could have lasted right up into modern times; it was surviving well enough until having to deal with World War I and everything that came afterwards. I've never understood why so many people on an alternate history website seem so fond of the idea that many historical events (like the fall of the Ottoman Empire) are inevitable; doesn't that go completely against the spirit of alternate history in the first place?