I just had this very same problem after testing a form that worked perfectly, form filled out and email sent to a gmail account.
After working on the form some more it stopped working. I figure out that at the bottom of the Message Body section (the area where you specify how the form content will display in an email) has this footer:
--
This mail is sent via contact form on http://your-domain-name.com
I deleted this line when reworking my form and after adding it again the form sent the email.
I'm not sure if this will work in your situation, there's plenty of web hosts out there that have trouble with CF7. I use Blue Host.