The length of time you have to drop a course is determined by the official Dates and Deadlines calendar set by the MU Registrar's Office every semester. The date on which you drop a course affects several things, including the refund you are eliglble for and whether the course will still appear on your transcript etc. Click the link above for add/drop deadlines. (The schedule for 8-week courses is located near the bottom of the page.)
Note: If you drop or fail to complete a course, you forfeit MU employee assistance and other financial aid, thus you are responsible for all fees incurred up to the time of your withdrawal.