HTTPS session not passing through F5.

If this is for browser-based communications, then generally speaking SSL persistence doesn't work (reliably). This persistence method uses the SSL session ID to control load balancing affinity, but that number will change whenever an SSL session is renegotiated, which happens quite often for browsers.

To summarize, in the absence of the ability to see inside SSL traffic, any load balancing product is generally limited to IP addresses to maintain affinity. There are some non-browser clients (of stateful protocols) that don't renegotiate their SSL sessions, where SSL persistence works, but guessing that's not what you need here.