Thank you for your post.
Is it possible there is a permissions problem? That would account for scripts being run to send emails, but the data would not be saved.
Is this happening to certain individuals, or is it random? Are these individuals able to save data some of the time? Is there a certain time of day when this occurs? Do the server log files provide any clue?
Did you test what happens if a user clicks the browser back button after he had submitted the inquiry?