Update: Oct 6, 2009 (and final)
Shareport still working without rebooting router. Good luck to everyone else trying to resolve the issue with their specific configurations.
Update: Sept 23, 2009
Maybe fixes must vary for different Dlink products and/or clients, but I am still working for 7 days with this one change: UNchecking "enable DNS relay".
Dlink 825
Windows Vista Ultimate, 64 bit
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Like the others, I tried this and Shareport is working for two days straight (better than before).
As for DNS, I simply rebooted my computer and it resolved the DNS issues on its own during the connection process. I don't know why you would have to do so by hand.