We are facing this issue where laptops are able to connect within premises to exchange but not from outside.
Activesync also stopped working for some people but not all.
This behavior occurred after we renewed our SSL certificates recently.
On one of the mobiles I got the following log:
Checking Certificate...Checking to see if server is self-signed :https://***.***.***.**
Server cert IS trusted, disabling accept all certs
SSL handshake aborted: ssl=119476e8: I/O error during system call, Connection reset by peer:Exception performing request
ActiveSync version check returned negative, but still trying for 12.1