Yes they do. When a better product arrives that gains enough traction, users migrate very quickly. Myspace, Altavista, Aol etc.
MySpace: Still going at https://myspace.com/
Altavista: https://en.wikipedia.org/wiki/AltaVista - shut down in 2013, 10 years after it was sold to Yahoo!.
AOL: Very much still alive at http://www.aol.com, owns sites like Huffington Post.
And in response to mattmanser, ICQ: Still going at https://icq.com/
They may not be the behemoths of the tech industry any more but they are definitely not dead. And the only one that is dead took a decade before it was shut down.
Sites with millions of users never die quickly.
Formspring failed extremely fast.
http://techcrunch.com/2013/03/15/formspring-the-pioneering-a...
It was one of the fastest growing services in Web history, and unraveled just as fast.
The existing service was completely shut down. The homepage is now some kind of funnel for another service.
And an example that wasn't market based: Megaupload. 180 million users, killed overnight.
Megaupload was killed due to piracy issues. A bit different.
Everyone used to use ICQ.
Twitter might be hard (impossible?) to successfully monetize to the point where it's actually profitable, but as a platform it still has a huge amount of value that lots of people would like to own. Platforms with millions of users never fail quickly.