I. Proper function isn't necessary for knowledge: Greco's counterexample
John Greco points out that there are actual cases of people with certain sorts of brain lesions that enhance their memory abilities. If so, then we have cases of knowledge without proper function, in which case proper function isn't necessary for knowledge.
II. Proper Function isn't sufficient for knowledge: Lehrer's counterexample
Keith Lehrer has applied his famous "Truetemp" thought experiment to Plantinga's proper functionalist account of knowledge. According to the thought experiment, physicians anesthetize a patient and implant a device in his head (unbeknownst to the patient) that causes him to reliably form very precise beliefs about the outside temperature. However, Truetemp has no special inner phenomenology associated with the beliefs; nor has he had occasion to check the reliability of his temperature beliefs (say, with a thermometer). Rather, Truetemp just finds himself having these beliefs some time after the operation (and again, he has no idea that the doctors installed the device in his head). So according to the thought experiment, we have a cognitive faculty that, when functioning properly, reliably produces firm and unwavering true beliefs when in epistemically congenial environments. Intuitively, though, Truetemp's beliefs don't count as knowledge. If so, then we have a case of proper function without knowledge, in which case proper function isn't sufficient for knowledge.
 Greco, J. 2003. “Virtue and Luck, Epistemic and Otherwise,” Metaphilosophy 34:3, 353-66.
 See Lehrer's chapter in Warrant in Contemporary Epistemology, especially pp. 32-33.