Is it possible to access stats about who and when disliked my page on Facebook? I looked through menu at Facebook, but I cannot find anything about this.
Well, now (2+ year later) with New Page Insights you can view at least some info about unlikes.
To access this data:
Go to the New Page Insights section, while being logged in to Facebook as your Page.
Click on Page Likes box title or navigate to Likes tab.
In third chart (Net Likes: What Changed) click on Unlikes below Benchmark in right box.
As description for this chart says, net likes are "pure" likes, that is likes–unlikes.