Well, I think I figured out what's going on.
In v5, the default login form apparently has other input fields. IE looks at the form to see if it's what it thinks is a login screen. After I created a new Login skin, dropped in the Account Login module and unchecked the host > remember me box, I was almost there. The final step was to find the skin and set dnn:search to NOT be visible. Once that input field was gone, IE decided this was an input form, and the "Save Password" message started coming up. It was already working in my current version because we don't use the "remember me" checkbox or Search.
In v6, I tried the same stuff, but that still didn't fix it. I noticed that cmdLogin in v5 was a "asp:button", but v6 changed it to "asp:linkbutton". I tried changing it back to a button, but that doesn't do anything because the generated HTML is "type=button" regardless. Normally an asp:button would create a "type=submit", but Telerik is different starting with 6.0.0. All "type=submit"s are forcibly changed to "type=button", and IE won't accept that it's a login screen if it's not submitted.
http://www.telerik.com/support/kb/asp...
As a test, I took the HTML generated for the cmdLogin input control, and pasted it in the login.ascx instead of the asp:button, and finally changed the type=button to type=submit. The "Save Password" message popped up!
I guess I'll have to see if I can come up with a more elegant solution, though.