I've been working on solving this for a few days and have found a
solution for my environment.

The problems was with the access of the autodiscovery service.
Specifically, if the client machine is
configured to use a proxy server then the autodiscovery fails which
leads to the multiple password
challenges.

The solution for me was to exclude the autodiscovery domain (https://
*ExhangeMachineName*) from the list
of sites checked by the proxy server. I already had the "bypass local
addresses" box checked but for
whatever reason that was not enough. Once I explicitly excluded the
exchange machine from the sites that went
through the proxy server the repeated password prompts went away.

Good luck.

-- Gary