Ok, how did you setup Exchange? Did you leverage the deployment guide and iApp from here?
https://devcentral.f5.com/wiki/iapp.Microsoft-Exchange-2010-and-2013-iApp-Template.ashx
I assume you did not try to setup SSL offload, as Exchange 2013 does not support it by default. I am guessing that there could be an issue happening with the SSL re-encryption. If you did not use an iApp, I suggest you set it up using the link provided. If you did set it up with an iApp, then I suggest trying to remove advanced profiles from the OWA Virtual server one by one to see at which point it starts working. By advanced profiles I mean NTLM, OneConnect, HTTP Compression, Web Acceleration, HTTP, and finally SSL. Once you find out which profile is causing the issue, it'll be easier to find a resolution. You should also feel free to open a support case to troubleshoot this.