Automatically save SMS text messages

Is there any iPhone app (that does not require connecting to computer/syncing/etc.) that automatically saves text messages as soon as they are sent or received? For instance, say I receive a message, and delete it immediately after reading it. Is there an application that will automatically save the text I received into the iPhone, to where I can open this app and view every text message ever sent/received even if I deleted it? Basically something like a keylogger that only records sent or received texts.

I understand that you can keep records of SMS by syncing to iTunes (or via another computer-based app), but I'm wondering if there is a way to store text history automatically within an app on the phone (similar to your call log being stored online at your carrier's website even after you delete the call log on your phone).