I had the same equipment senario you described until recently without issue. I have since changed to a gaming router with a faster ping response time.
You should place the ooma device behind the router and set it up with a static internal IP address. You should also set a priority number of 1 for the ooma device's ip address in the 655's menu for priority settings.
You also need to port forward the following ports in oyur dlink router and direct them to the internal ip address you set for the ooma device:
UDP 53, 123, 514, 1194, 3386, 3480, 10000-20000, 49000-50000
TCP 53, 443
As far as the slingbox settings go, you alaso need to assign it an internal static ip address from within the dlink dir-655's web portal interface and port forward TCP port 5001 to the address you assign.