DNS Nameserver's DNS/IP Change

My server and my secondary DNS server is down due to hurricane
CHarley...
The entry at Network solutions, for my dns server
(ns1.brainscanstudios.com), is currently pointing to 207.30.114.50.
207.30.114.50 is a server in Orlando that may be down for a while.
However, my DNS for the domain "brainscanstudios.com" is handled by an
external DNS company. If I have the external company update my DNS for
ns1.brainscanstudios.com to point to a new server (with new IP), that
is up and running, will Network solutions update their record of the
NS1.Brainscanstudios.com's IP to the new IP, or do I have to do that
manually?
If they don't do that... the next question is why, since it is the
same server name "NS1.brainscanstudios.com", why wouldn't they just
update the IP for it, like DNS does?

THanks for the help