Is there an iPhone application that will allow me to save all the text messages that I already sent? Just to get a copy whenever I accidentally deleted it. Any recommendations?
Try the PhoneView for your iPhone.
It will allow you to create a backup.
It will let you save your applications, text messages, iMessages, voicemail, contacts and everything.
As you asked you are looking for an iphone application  that saves all the text messages ,according to me you can download Syphone .Syphone is an opensource software . By using Syphone  user can back up, save and view user SMS messages. By using Syphone user can view SMS conversations, including those SMS that have been deleted from user iPhone.
