If you're decrypting the SSL on LTM you could use cookie insert persistence instead. This is generally a better method than SSL session ID persistence as it is not subject to the browser using a new session ID.
But I'm surprised to hear that all requests get persisted to the same pool member with SSL session ID persistence. Each browser, even if connecting from behind the same proxy, should negotiate an SSL handshake with a separate SSL session ID. Or are you using server SSL also? If so, see SOL3062 for the requirements for using SSL persistence:
sol3062: Using SSL (Session ID) persistence
http://support.f5.com/kb/en-us/solutions/public/3000/000/sol3062.html
Aaron