Like other mobile phone instruments iphone allocates particular space(MB) to store SMSes. iPhone stops receiving new SMS once allocated memory is full. An iPhone user have to delete old SMS to be able to receive new ones. There is one more way to continue receive new SMS without deleting old ones.
Users can take backup of important SMS into PC instead of delete them. There is a tool to get this done easily. This iPhone software can help to take backup of all the stored SMS or selected SMS.

1: Download and install this tool
2: Get iPhone connected to computer.
3: Run the iPhone SMS software. All the SMSes will be displyed on screen same way you can see in iPhone.
To check out the detail associated with SMS just click on particular contact.
You will have two options. You can either take back up of all the SMS or of just selected SMS. To BackUp/transfer all the SMS click copy all SMS and to save selected SMS click Copy From Who.
SMS can be saved in two file formats, namely TXT and ANTS. Benefits to save SMS in ANTS file is it can be made password protected.