<p>Yes, you can stay in Canada legally with only your study permit. </p><p>Visa - used only at Canadain Customs when you entering Canada from a foregin country. </p><p>Study /work permit - your legal status in Canada. Legally, you always required to have a valid permit while staying at Canada. </p><p>In your case, apply for study permit extension now and apply for visa extension at least a month before your departure from Canada </p>