Came across your request. Let's see if I can help.
I noticed that the default source looks like this:
<input type="submit" value="Trimite" class="wpcf7-form-control wpcf7-submit" data-value="Trimite">
But, after clicking the submit box, the source looks like this:
<input type="submit" value="" class="wpcf7-form-control wpcf7-submit focusInput" data-value="Trimite">
I noticed the value is blank between the quotes in the source after clicking. Not sure if that is the issue, but wanted to see if that was the issue. I noticed when I did an Inspect Element and edited as HTML and added the value, Trimite, back in-between the quotes, the button worked.
And, I noticed that in my own contact form 7 that the value continues to display after I click on my submit button. Therefore there might be something wrong with the code or some css with the value disappearing when focusInput.
I hope these are a couple of clues that will help solve this problem for you. Good Luck!