Weddings and other formal events require those invited to RSVP. It is proper etiquette to respond quickly, whether you are accepting the invitation or not. Some invitations include printed response cards that make it easy to note whether you'll be able to attend the event: Simply check off the box that states you will not be attending and drop the card in the mail. Other invitations require a formal, written regret as your RSVP.
Make sure you are absolutely unable or do not want to attend the event before you respond. Changing your answer later on may upset event arrangements.
Write your letter in the third person. Most formal invitations are written in this style, and your RSVP should be written in the same fashion.
Begin the letter by congratulating the couple, if it is a wedding invitation. If not, simply express your thanks for the invitation.
Proceed with your regret to the host. Use wording such as "John Smith regretfully declines the invitation of Mr. and Mrs. Host for the first of September."
Do not include an explanation for your absence, unless you choose. If you feel obliged, you may apologize for your regrets and explain they are due to a prior commitment, family obligation, illness, etc.