I am having the exact same problem, I have spent days trying every certificate integration angle I could think of and every time it does the same thing below. I have confirmed that the ActiveSync server address will prompt for the cert if I enter via the browser so it can see and communicate with the server but the mail app just refuses to prompt.
From JasonH:
I have windows 8.1 and the updated Mail application.
No matter what method I try, or account I try to add, I cannot get the mail client to ask for use of a certificate for EAS auth. It consistently asks for username and password and then just notes that I "may need a certificate to connect this system."
I have a certificate in my user store. I've verified that and that I have the private key. I have other applications which work with that certificate. What am I missing?