Most often, Blackbaud NetCommunity is configured to connect to appropriate resources via domain name and not IP address.  As such, there should be very little effect on changing the IP address of the Blackbaud NetCommunity webserver. *

Check the following areas to confirm necessary services are being requested via domain name:

In Blackbaud NetCommunity > Administration > Configuration:
The Raiser's Edge : URL
Custom Service : URL

In Blackbaud NetCommunity > Administration > System Options:
General : Site URL

In The Raiser's Edge > NetCommunity > Options > Connection Settings:
URL

*It will be necessary for you to update DNS records for appropriate domains to point to the new IP address.  Contact a qualified IT professional or your Domain Registrar for assistance with this point, which is beyond the scope of what Blackbaud NetCommunity support can assist