Subsequent calls bypass the F5

I am not disabling the pool member.  I remove it from the pool completely.  I will try a force offline first to see if that will work differently.

I think that this might be the issue. Removing the members from the configuration would prevent new connections from reaching the members, but the existing connections might still be retained (some parts of the configuration is "cached" on a connection basis).

As I understood One-connect, it would keep the connection from the client request at the F5, instead at the server that is fulfilling the request.  I think One-connect is not working because if I turn off the server that is fulfilling the request, it is able to send a Connection Forceably Closed error message to the client.  (Showing that the client is directly connected to the server that is fulfilling the request.)

When you mention "it is able to send a Connection..." are you referring to the server sending it, or the F5?