Can't submit a form in an iframe

There is a scientific event with a registration form embedded in an iframe: http://enginfest.sfedu.ru/registration/.

If you switch to the login tab (Вход) and try to submit any data you will see the problem. The login form does not send a "post" request to the URL specified in "action" attribute of the form tag. Interestingly enough, the registration form from the image works fine. I've compared both forms and haven't found an essential difference.

I used the latest version of Safari from El Capitan OS. That form works as it supposed to work in Google Chrome and other modern browsers.

I want to change a layout of the form to make my visitors able to sign in. Help me please to resolve that problem. Thanks!