Hello,
I am not implying, I am telling you that it is not working properly, but not because of the Asterisk, it is because of the SIP protocol.
Anyway, if you are using a dynamic public ip (that changes all the time) you will need to install a client that will update your ip in dynamic services (dyndns, no-ip etc.) if you want to use a domain instead an ip.
Thank you,
Daniel Friedman
Trixton LTD.