The Java EE bean annotations such as @PostConstruct only apply to container-managed beans. If you are simply calling new BlogEntryDao yourself, the container isn’t going to intercept the creation and call the @PostConstruct method.
(Furthermore, you’d be better off using @PersistenceContext or @PersistenceUnit instead of manually fetching the EntityManagerFactory in your initialize() method, and you should be creating an EntityManager for each call to addNewEntry(), since they’re short-lived. Making these changes would eliminate the need for initialize() at all.)