2004, Devon Mack Wild, Pick-Up Lines That Work, ISBN 9780595323685, p. 28 (Google search result):If she doesn't smile with this pick-up line she might be suffering from a case of permafrown.
2009, Stephen Frey, Forced Out, ISBN 9781416549642, p. 219 (Google preview):Usually the kid wore a mean permafrown and stared everyone down.
2013, Jessica Bird, Lover At Last: A Novel of the Black Dagger Brotherhood, ISBN 9781101607718, (Google preview):That face . . . was so grim, with hollows under the cheekbones and a perma-frown that suggested the guy hadn't slept in seven days.