AirPort Software 1.1 and saving passwords to the Keychain: only partially successful?

Wysmar Clealand notes that Apple TIL article (#58531) states that AirPort Software 1.1 update allows Base Station passwords to work with Mac OS 9's Keychain. However, he found that this only worked if he had an Ethernet connection to the Internet. With a dial-up connection (or likely any connection where the IP address changes each time you connect), the AirPort software would still "ask for the password every time I open the application and, what's more irritating, it will even save multiple times to the Keychain if you leave the 'add to key chain' check box marked." He was connected to the Base Station via a Silver WaveLAN card.