I think this problem began with WP CleanFix version 3 (I'm currently running 3.02), but I'm not certain of that.
On a WP site, Links are assigned to Link Categories. (Beginning with v 3.5, the Link functionality is hidden unless the site was previously using Links.) On my site, WP CleanFix flags these assignments under "Consistent Terms/Relationships". When I allow it to "repair" them, it deletes the Link Category assignments, causing the links to no longer appear on the site (until I add back at least one link category assignment to each).