Don't store their username or password in a cookie. Always assume that everyone on the internet can see every cookie on a person's computer. What you should do instead is save the session_id and the IP address they accessed from to your MySQL table, then save the session_id to a cookie. Most browsers will clear session variables when you close the window, but they will not clear cookies. Therefore you first check the session (are they currently logged in), and if they're not logged in then you check the cookie (were the logged in before, and more importantly- was it from this IP address?)
Of course if they have a session_id but they're not at the proper IP address, make them log in. They could just have an ISP with dynamic IPs, or they could have been listening to network traffic and they're trying to get into the admin user without a password.