Nimbostratus
Cirrostratus
When using cookie insert persistence with a 0 timeout, LTM will only set the cookie in responses when a new load balancing selection is being made. This is expected behavior as the client should continue sending the same persistence cookie on each request for the duration that the browser is kept open.
The most common issue with cookie persistence is not having a OneConnect profile. Do you have a OneConnect profile added to the virtual server? This is necessary whenever you're doing per HTTP request persistence. If you're using SNAT on the serverside connection, you should use a /0 source mask on the OneConnect profile. If you're not doing source address translation on the serverside connection, create a custom /32 source mask OneConnect profile and add that to the virtual server.
See this wiki page for details on why this is necessary:
http://devcentral.f5.com/wiki/default.aspx/AdvDesignConfig/oneconnect
Aaron