We are on a 6 month Business Visa in Riyadh, Saudi Arabia.?

However, we are only allowed to stay for 30 days at a time then we must be out. We cannot affort to fly back to South Africa once a month. If flying out to Musmac will our visas be stamped? and how quick can we obtain a visitors visa for Musmac. We only have 10 days left. Where do we apply?