Unable to save credentials when connecting through an RDP Gateway

I've recently set up an RDP Gateway, but my users are unable to connect to it when the "Remember my password" box is checked on the Enter your credentials screen.

If the box is unchecked, the connection proceeds without issues.  The same credentials are used for the RD Gateway Server and the RD Session Host and both are running Windows Server 2008 R2.  The clients are all using Windows XP SP3.  We've tried it with Remote Desktop Client versions 6.0.6001.18589 and 6.1.7600.16385, and get the same issue.

If the box is checked, no errors are displayed, but the Enter your credentials screen is displayed repeatedly.

Any ideas what could be causing this?