iRule to send a cookie with every HTTP request

Someone correct me if I am wrong here, but the cookie once it is sent to the client exists on their box until the timeout value has passed or it is manually deleted. So once one is set it lasts until the timeout value has gone passed. This generally only happens when the connection is idle though. If any info is passed and the cookie is used the time out value is generally reset back to the max time out value and the countdown starts over. If a cookie must be present but needs to be new each time, then the only thing I can think of is to change the cookies timeout value to 0 (not sure what this would do, probably just disable your persistence) or you could try to delete the existing cookie that you just set, every time you see it come in with an HTTP request.

 when HTTP_REQUEST { 
 priority 100 
  Check to see if the cookie exist in the request
 if { [HTTP::cookie exists "insert-cookie-name"] } { 
 Delete the cookie 
 HTTP::cookie remove "insert-cookie-name"  
 } 
 when HTTP_REQUEST { 
 priority 200 
 set persistence cookie insert "insert-cookie-name" } 
 } 
 }