Thanks both daniel and pclinmike, I don't use Update-Notifier. This is the Notifications located in my System Tray. Your suggestions prompted me to pursue modifying it in the tray. The tray can show Application Status, Communications, System Services, Hardware, and Miscellaneous. I'll try deselecting each in turn and see what turns off the network messages.
My network stays up when my desktop suspends. I think when my desktop resumes, it looks for the network before the network card gets it negotiated. Usually it is a matter of seconds, but I get the unwanted messages.
Thanks for the ideas,