The WordPress SEO plugin by Yoast has a bug in the settings for Permalinks. If you try to uncheck any of the options, they will not take.
I found this out after I figured out that I should not have checked "Redirect attachment URL's to parent post URL." (because I want to keep my attachments as separate pages) and I should not have checked "Redirect ugly URL's to clean permalinks." (because some of my posts have multiple pages and now they are broken).
Anyway, if I try to uncheck these options, the boxes stay checked, and the settings will not turn off.