This article can now be downloaded: Marco Grandis - Robert Paré, Persistent double limits, Cah. Topol. Géom. Différ. Catég. 60 (2019), 255--297. http://cahierstgdc.com/index.php/volume-lx/ (in: Issue 3, second article) Abstract. Continuing our study of double limits in weak double categories, we investigate the 'invariant case' of persistent double limits, which is related to flexible weighted limits in 2-categories. Regards, Marco and Bob [For admin and other information see: http://www.mta.ca/~cat-dist/ ]