I've setup certificate based authentication for activesync on Exchange 2013. We're using primarily iOS devices and that's all I'm testing with for now.
I apply the profile using Apple's iPhone configuration Utility, install the profile on the phone and my mailbox syncs as expected. I can send and receive messages for a short time, somewhere between 2 and 5 minutes. After that I cannot get a connection again and get the message "The connection to the server failed." I am able to access the server through safari so network connectivity is OK. The only way to regain a working activesync connection seams to be either rebooting the phone completely or instructing the iPhone to "Reset Network Settings" which also ends up rebooting the phone.
I have verifiied that "Include inheritable permissions from this object's parent" is selected in the users AD security settings which was the only item I have found that may relate to this error in my searching.
I did have certificate based auth working in my Exchange 2007/2010 environment and also in my Exchange 2013 test environment.
The Exchange remote connectivity analyzer test for activesync fails but only because of the certificate auth which it doesn't seem to be setup to handle. Everything else passes.