In EJB3.1 which is available in JBoss AS6, you have @Singleton beans which can hold state. @Singleton beans can also use the TimerService unlike @Stateful. So give it a try in EJB3.1
Thanks for answer Jaikiran. Unfortunately I cannot use JBoss AS6 because other parts of application has been designed to work with JBoss 5.0.0.GA and uses some non-standard features. Because of this I cannot take into consideration migration to newer application server.
Secondly I need multiple instances of this beans, because each one holds connection to another router (with all connection-related properties).