It all started on comment #125 on the 661 comment behemoth Ratites in trees: the evolution of ostriches and kin, and the repeated evolution of flightlessness (ratite evolution part II). Permian Bears are the logical consequence of a world with vicariance and no dispersal, although strangely Grehan1896 didn't seem to think so.
One possible antecedent is an article titled "Petrified Footprints: A Puzzling Parade of Permian Beasts" that appeared in Smithsonian Magazine in July 1992, a transcript of which is available. In it, Jerry MacDonald is described as "reluctantly" admitting that some tracks in Permian strata look bear-like. This rather shaky comparison has been referenced by at least one Young Earth Creationist websiteGenesis Park and one forum citing that website specifically uses the phrase "Permian Bear" EvC Forum.
Tapinocephalians are compared to "Permian bears" on a therapsid website.