I figure he's either using 6to4, or Teredo or he has IPv6 privacy on. Note that the original v6 does still work for a while even with privacy turned on, but I don't really like it.
To turn it off, you can issue the command: netsh int ipv6 set privacy disabled
Anyways, if for whatever reason you can't get your v6 to stop changing, I'm not sure if any of the dynDNS services support v6 yet or not. DynDNS.com has an IPv6 NS, but doesn't seem to have dynamic updates.
One thing you could do is configure your own BIND deamon and domain (you'd have to reg a domain of course and pay for it, unless there's some free service that does delegations for subdomains or something). the configure your BIND daemon to accecpt dynamic updates, and windows will update it with its hostname, both for IPv4 and IPv6. Then you could get to your host via that.
EDIT: Googling around, I just found http://www.dns6.org/
which appears to offer dynamic ipv6 DNS support. May be others out there too. I think http://freedns.afraid.org/
also does it, but not clear from their page.