lots of iPhone users have the same trouble. that is they can't backup the SMS to anywhere when the SMS box is full, then they have to delete all of them to prevent iPhone rejecting new SMS receiving. here is a useful tool to help solving this problem.
Tansee iPhone Transfer SMS can provide you:
* Backup SMS in iPhone to computer before iPhone reject receiving new SMS.
* View and Manage old iPhone SMS in your computer.
* View SMS in Text file format (.txt file), ANTS file format (.ants file), MHT file format (.mht file)on PC.
* Password protection support (ANTS file only).
* Edit SMS (ANTS file only)
* Print SMS (MHT file print by IE).