CF7 does not save submissions to the WP database - there is a popular plugin http://wordpress.org/plugins/contact-form-7-to-database-extension/ that does that.
Normally getting CF7 submissions into the WP database via Contact Form DB is very reliable. Lots of WP Developers use it at as a fail-safe backup for when forms don't get through via email (which can be a much tougher proposition for some due to their local Server Email configuration).
If you include a link to your Contact Form 7 form others here may be able to look at your particular problem in more detail.