Cirrostratus
Nimbostratus
To my knowledge you cannot do what you are attempting with the BigIP LTM.
The LTM will try and keep your Client connected to an available pool member. If one goes down then you can make the response to the node failure automatic for the Client (Action On Service Down – Default is None. I suggest changing this to Reselect).
The Cooke Persistence is how the BigIP LTM keeps track of the server that the Client was Load Balanced to. If that server goes down, then the Action On Service Down should select a new server and re-issue a new cookie. That behavior is correct.
If you are looking to keep the Session Information consistent then you will need to use a different methodology (Store Session Information in a Database, Session Cookie, etc.).
The BigIP LTM does not keep session information for the client in response to a server failure. It can keep the persistence and state information current between a load balanced pair of BigIP LTM’s (Virtual Server configuration – Connection Mirroring), but there is an associated performance cost for doing this.
Hope this helps.