F5 Load Balancer using Cookies to route traffic.

What cookie method are you using? Hash?

Assuming so, The cookie gets mapped when the server has a set cookie in the response, the first response from a will create the mapping, so when the second occurs it will already be mapped. This is a bit different than you described, the mapping does not occur when the client request comes in with a cookie, but when the server responds with the cookie.

See http://support.f5.com/kb/en-us/solutions/public/6000/500/sol6586.html for more info.

When a member is down, the F5 will send requests to another member just like no cookie was present(dependent on your action on service down setting). That server will set the cookie to its value and persistence is now established with that server.

Not sure if you can clear the cache, I don't think you would want to anyway.

Also be aware that if a client is idle for the entire time a server goes down and then comes back, when they finally make their request with the old cookie, since that server is now back they will land on it again. Probably not a big deal, but sometimes I have people down a server for 1 minute thinking they will get everyone off of it and then re-enable it and are surprised to see how many people are still stuck to it. If they don't make a request while it is down, they won't get a new cookie value and their old cookie value will now be valid again.