Maintenance mode: sticky HTTP sessions

Take a look at K13310.

If you disable a pool member, it will allow existing connections and persistent sessions to continue. New sessions that do not have a persistence record will not be balanced to that member.

You can either disable the pool member manually (per the Knowledge article), or configure your pool monitor with a recv-disable string and modifying the monitored file appropriately. (Advantage here is allowing the web server administrator to disable pool members when they need to perform maintenance, without having to contact the BIG-IP administrator to do it manually.)