In terms of keeping the old site around forever... just dump it after a reasonable amount of time.
You can either email them a replacement .wyc file, or supply a link to a full downloadable installer (assuming you guys produce one). They'll get some sort of error about being unable to check for updates, but that doesn't sound insurmountably bad to me.
[NOTE: I'm assuming that your software supplies a way for them to contact support that will continue to work after your domain name changes. Otherwise, you may be stuck with maintaining the old site for much, much longer]
Of course, we'd all be best served by making sure that our updates are being hosted in a domain name that we have complete confidence in controlling forever, so as to avoid this issue entirely