Sounds like spider mites. Checking on-line shows that
"Spider mites are usually not killed by regular insecticides, so be sure to check the pesticide label to see if "miticide" is present. Pesticides claiming "for mite suppression" are usually weak miticides and will not perform well. There are few products available to the homeowner. Dicofol (=Kelthane) is registered for over-the-counter use but is difficult to find. Acephate (=Orthene), dimethoate (=Cygon), chlorpyrifos (=Dursban), diazinon, disulfoton (=Di-syston), and malathion have over-the-counter product labels but are considered weak miticides."