I ran into the same problem with a similar deployment (LTM performing client-ssl & server-ssl before forwarding traffic to an ASA 5580). The ASA firewall is running v9.1.4 & AnyConnect v3, and I found the following link that describes the problem:
http://www.cisco.com/c/en/us/support/docs/security/anyconnect-secure-mobility-client/116881-technote-anyconnect-00.html
I tried using the workaround on the firewall as outlined in the link above, but none of them work for me. Finally, to fix this issue, I created another virtual server which load balances DTLS (UDP 443) to the ASA firewall, and the AnyConnect issues disappear.