From your description, I do not think the two things are related in any way. (At least I can't imagine how they could be.)
That said, you may want to verify Google Webmaster Tools have not reported any warnings and/or errors. (GWT reports warnings and errors for many things with your website including sitemaps, so you should be able to see it there if Google believes anything is not acting correctly.)
Are you sure your website hasn't been hit by an algorithmic update like Penguin, Panda or similar? (Which has a tendency to cause problems in organic search for many website owners?)
There's also an increasing amount of "encrypted_search" / "not provided" in everyone's Google Analytics:
http://blog.kissmetrics.com/unlock-keyword-not-provided/