So let me get an idea of how your devices are connected...
What ISP Modem do you have? Stand Alone or built in router?
What ISP Modem make and model do you have?
ISP modem>DIR-655><Cisco Router<>Vonage device?
If this ls correct, I would first try inputting the in IP address the Cisco router gets from the DIR-655 into the DMZ on the DIR-655 under Advanced/Firewall. If the Vonage device gets it's own IP address from a router, I would not use the Cisco router, and connect the Vonage device to the DIR-655 using the LAN ports between the two, then inputting the IP address the Vonage device gets from the DIR-655 into the DMZ.
Looks like your having some double NAT issues here with having 2 routers on the same line. The DMZ should help keep the Vonage phone service going well for you...
When I used a AT&T Microcell I had to use DMZ and it worked well when I had it.
Theres a Vonage FAQ as well:
http://forums.dlink.com/index.php?board=304.0Keep us posted.