Hi Tad Rhodes,
I am afraid this scenario is currently not supported and is hard to implement manually, because there are quite a lot of event handlers attached to the RadTextBox textbox, which should be switched (reattached) when the user enters or clears the password.
However, there is a relatively simple workaround, demonstrated below. If for some reason you can't or don't want to use it, I can only suggest you to use a regular asp:TextBox styled with RadFormDecorator (or ordinary CSS styles) to look like a RadTextBox with the same skin.
the Telerik team