Canadian going to Beijing, but coming from South Korea. Is there really a 6 months ARC rule?

My husband and I have booked flights to Beijing from Seoul for June. We're professors in Korea, but are Canadian. We will resign our contracts, but our ARCs expire (need to be renewed) in August. Does this mean we can't get a VISA? If so, what is the mentally behind this? Most people travel on their vacations, which typically come at the end, not the beginning, of contracts.