I had a misconception of @ConversationScoped.
Conversation should start before visiting a given link.
Means that if one visit a link, with no conversation started previously, the bean will act similar to a @RequestScoped bean. Therefore refreshing one page attached to a @ConversationScoped will create & destroy each time.
Solution goes to start the conversation before visiting the link, so ?cid=10 will be included in the URL.