Thanks for your replies. I think that esmi may be correct. I looked at the CF7 docs and found this info on an extension that we do not appear to have installed.
>>Contact Form 7 to Database Extension
Extension to the Contact Form 7 plugin that saves submitted form data to the database.
Takes submissions from Contact Form 7 plugin, saves them in the database and allows you to export the data.
First a disclaimer: I am not the maker of Contact Form 7 or associated with it's author.
That being said, I think Contact Form 7 is great...except for one thing. It does not save its information to the database. And if you get a lot of form submissions, then you end up sorting through a lot of email.
Fortunately, the author of CF7 created a hook. So I wrote a plugin that hooks into CF7 and saves all of its form submissions to the database. You need to have both CF7 and this plugin installed and activated.
This plugin also puts a menu item in the Administration Plugins menu where you can see the data in the database. It's pretty rudimentary but does the job.<<
So I'm thinking that, because that extension is not installed, the form data has not been saved to the data base. I'm not sure if there's any way to retrieve this potentially lost (by e-mail) form data. It doesn't appear that it has been stored in any part of the WP database. If it has been stored somewhere in the database I don't know where to look for it.