Latest(for the moment of article publication) Contact Form 7 plugin update(4.6) broke integration with "Bootstrap for Contact Form 7" add-on which used to style forms according theme design. This situation leaded to unexpected behavior of contact forms on some websites.
We are working with plugins authors to solve issue, but for now we haven't fixed it and our main recommendation is to use previous(4.5.1) version of contact form 7.
You can download it from this link. To install it just remove your current version and then make a fresh install from downloaded file.