My apologies for not responding sooner. I must of missed a notification about your post.
@Yumiko and @urbanjurist
Make sure your Form settings are correct.
Here is a screenshot from the contact form on our site as an example.
https://www.dropbox.com/s/4r18klceli031oy/contact-form-7-settings.PNG?dl=0
Also, make sure the form emails are not going to your Junkmail folder. This can happen sometimes.
Let me know if that fixes the issue.