I have this problem too, and I don't have Antivirus installed on one of my computers, I tried to disable the firewall too, on that computer but that didn't make any difference.
If I reboot the DIR-655(Firmware 1.31 HW: A4) I can connect fine even if the firewall is enabled, and it works for a while, but if I try to connect again later on, the shareport utility shows my printer as available, but when i try to connect it says: connecting, then receiving status, and then shows it as available again. I have also experienced that when I switch the printer on, the utility doesn't show the printer at all. A reboot of the DIR-655 helps on this problem too, but this problem is rare compared to the connect-disconnect problem.