After completing the XPSRegClient portion of Admin UI registration, the client name specified in the XPSRegClient command cannot log into the Admin UI to complete the registration. The Policy Server's smps.log is showing handshake failures upon each login attempt.
Customer had earlier applied a patch to the Admin UI host OS that caused the RNG daemon (random number generator) to stop running. The caused entropy to run low, which can cause a wide range of symptoms whenever a process calls for entropy, such as a login attempt which requires encryption.
Restoring the RNG daemon resolved the issue.