On the Guardian, Charles Arthur has totted up the lifespan of 39 products and services that Google has killed off in the past due to insufficient public interest. One interesting finding is that Google is becoming less patient with its less popular progeny, with an accelerating trend to killing off products that aren't cutting it. This was occasioned by the launch of Google Keep, a networked note-taking app which has the potential to become quite central to your workflow, and to be quite disruptive if Google kills it -- much like Google Reader, which is scheduled for impending switch-off.
So if you want to know when Google Keep, opened for business on 21 March 2013, will probably shut - again, assuming Google decides it's just not working - then, the mean suggests the answer is: 18 March 2017. That's about long enough for you to cram lots of information that you might rely on into it; and also long enough for Google to discover that, well, people aren't using it to the extent that it hoped. Much the same as happened with Knol (lifespan: 1,377 days, from 23 July 2008 to 30 April 2012), or Wave (1,095 days, from May 2009 - 30 April 2012) or of course Reader (2,824 days, from 7 October 2005 to 1 July 2013).
If you want to play around further with the numbers, then if we assume that closures occur randomly as a normal distribution around the mean, and that Google is going to shut Google Keep, then there's a 68% chance that the closure will occur between April 2015 and February 2019. Even the later date wouldn't be much longer than Evernote - which is still growing - has already lasted. Is Google really that committed to Keep?
I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.