Do people say why they decline a paper review request?
Established scientists receive a large number of review requests. A few years back I decided to tally the review requests I received, and the number I accepted. In the end I received 112 and accepted 28 over the course of a year.  Add to that the editorial work I did for three journals and you get an awful lot of uncompensated, unrewarded time invested for the good of the field. (I typically spend about eight hours a week on reviews and editorial work.) So yes, I declined a large number of review requests every year, many of which I would have been well qualified to handle. When the editorial system allows, I try to at least leave a note explaining that I'm too busy, but as jakebeal notes, this is not always an option. 

So yes, qualified reviewers can and do turn down many review requests, often without providing an explanation. As an editor, I know that if I ask well known researchers this will happen as often as not, and I don't mind that one bit. What I do dislike is when people don't bother to click the "decline" link on the review request, and force me to wait for a week before giving up and trying to find a new reviewer. This slows down the review process and ultimately slows down science for everyone.