Don't wait too long or it will cost you an extra $15 (yeah, I waited too long).
Do it before the expiration date.
If you wait more than 6 months after it expires, you have to go through the whole new application process.
Here is the Mississippi law on late renewals:
A licensee who fails to file a renewal application on or before its expiration date must renew his license by paying a late fee of Fifteen Dollars ($15.00).
No license shall be renewed six (6) months or more after its expiration date, and such license shall be deemed to be permanently expired.
A person whose license has been permanently expired may reapply for licensure; however, an application for licensure and fees pursuant to subsection (5) of this section must be submitted, and a background investigation shall be conducted pursuant to the provisions of this section.