client authentication certificate

Mike, you cannot terminate the SSL between the client and server if the server requires a client certificate. The client must digitally sign a piece of information and send that to the server during the handshake. A digital signore uses the sender's private key to encrypt, so if you decrypt and attempt to re-encrypt at a proxy, the proxy wouldn't have access to the client's private key.

At a minimum, you'd have to switch into layer 4 load balancing mode, with no client or server SSL profiles, and nothing more than source address for persistence.

You could optionally move the certificate authentication to the F5 with the Access Policy Manager module, and perform some other type of authentication to the backend web servers.