Gary,
No ISY doesn't lose power when the router does. Yes NAT is enabled and my router is set up so the ISY gets the same private/reserved internal/local IP address every time.
Michael,
Internal/local IP address does not change, as described above.
Also I checked the router and the port forward is correct in the router with the right IP address and port combination in the tables.
I will try the static IP address as suggested but this doesn't make sense to me. The router has the correct local/internal address and correct Port Forward in its tables. The only difference I see is when I go to the ISY and click on help it has the old external/internet IP address and things don't connect remotely.
Appreciate the help, thank you.