Pretty sure this idea that Facebook can "predict" when people will break up was based on research by Lee Byron and David McCandless of 10,000 Facebook status updates with the terms "break up" or "broken up", presented as a nice graph[1] as part of a TED talk[2].
[1] http://www.informationisbeautiful.net/2010/peak-break-up-tim...
[2] http://www.youtube.com/watch?v=pLqjQ55tz-U (skip up to 6:30)