Session Timeout

Do not forget that the BIGIP terminates client side and reinitiates server side connections - it's a full proxy. Now this behaviour also depends on what type of virtual server you are actually using. It also depends on which protocol we are talking about ... For instance, HTTP protocol is short lived, unlike protocols such as FTP.

With that said, I'd take a fairly educated guess here and say that you can't achieve this (and probably not even recommendable) through the F5BIGIP. If anything, I'd try to keep the session open sending traffic every x number of seconds, from the client itself.

Hope this helps.