Persistence Profile Timeout Element

My understanding:

F5 will discard persistence key:value from its persistence table after timeout and hence, can't make a decision if the client presents the same cookie after timeout. New load balancing decision will be made with new cookie.

Why do you want to set "indefinite" timeout ? If you are just looking for session persistence, you can utilize cookie insert. With indefinite timeout, I would expect uneven load balancing and depending on the number of connections, possible random loss in persistence if there are too many persistence table entries.

In my opinion, when deciding on persistence timeout, your choice should be based on application requirements - how long should a client be persisted for the session to complete successfully.