I was about to post about the same issue on iOS. Safari on Mac also has the same issue. Submitting the form does not send the form and just results in spinning icon. On Chrome and Opera for Mac the forms work as expected.
I have just come across this too. I thought it might be something to do with Google Recaptcha, removed that put in a simple math question same result. Spinning wait symbol.
Just to be clear here, the behaviour on a iPhone using Contact Form 7 is what I am reporting here. Latest IOS, in my case an iPhone 6. The form bounces down to the bottom of the footer for the site. Not sure why. RIght now as far as I can tell, you cannot submit a Contact Form 7 from an iphone, and if the other reports here are correct, from any Apple device.
The author addressed the issue here: https://wordpress.org/support/topic/no-confirmation-message-on-safari/#post-10268881
It’s a webkit issue that Apple must fix. Until then, remove the attachment option from your forms.
Thank you for the feedback.
I have also observed that if the attachment option is removed, and Google Recaptcha is in the form it still bounces down to the footer of the site at the point where you check the I am not a robot message. The user has to scroll up to click on the enter/ submit button to post the form. Is this related to the webkit problem as well? While the form works in this case, it is misleading to the user. On checking the box, they still have not sent the form, and have to scroll back up to the form to send it. I have removed the recaptcha function from the form. Now it works fine, however I would really like to to have it in there.