To write a letter requesting an extension of leave will need tact, diplomacy and a good, genuine reason. Remember it is not the divine right to be granted the extension and certainly not guaranteed. This will likely cost the company a significant amount of money in having to replace you for the extended time or result in work colleagues having to take up the slack, so try to be as gracious as possible, apologetic and have a really solid reason for the request. You should also determine how important the extended leave is.
It is likely that you either need the time off for something important, or would like the time off to do something like travelling or charity work. Your letter should look something like this:
Dear [insert name of contact]
Firstly I would like to let you know how appreciative I am that you allowed me [here you will need to state the amount of leave and reiterate the reason]
I feel it fair to inform you that I will be unable to return to work from [insert original return date] as agreed but unfortunately...
I am writing request a further extension to my leave as...
[the body of the letter should go on to explain the circumstances which have meant you require the extended leave and how much time you need in addition to the time already taken]
Thank you for understanding at this time
Yours sincerely
[Your name]
It is likely that you either need the time off for something important, or would like the time off to do something like travelling or charity work. Your letter should look something like this:
Dear [insert name of contact]
Firstly I would like to let you know how appreciative I am that you allowed me [here you will need to state the amount of leave and reiterate the reason]
I feel it fair to inform you that I will be unable to return to work from [insert original return date] as agreed but unfortunately...
I am writing request a further extension to my leave as...
[the body of the letter should go on to explain the circumstances which have meant you require the extended leave and how much time you need in addition to the time already taken]
Thank you for understanding at this time
Yours sincerely
[Your name]