2.5: cannot upload images (site is secure – https://…)

I run several WordPress Blogs on an “intranet” – which means that access to the webspace requires a login and the URL’s all begin with https://
Apache 2.0.55
PHP 5.1.2
(Redhat Linux)

Prior to upgrading from 2.3.3 to 2.5 we were able to upload images without difficulty. However, in 2.5 this fails. On Windows, when the upload starts, the user is asked to login (this is the little alert box) as a user on the server (not a WP user); on Mac 10.4/Firefox, it just displays an error saying that than error occurred, please try later.

I have looked at the server logs, but I can’t seem to find the error yet.
I have checked, and the uploads directory and it’s subdirectories are (shudder) world writable. So, I don’t think it’s a file permissions issue.

My suspicion is that somehow the js that controls this function isn’t coping appropriately with the https.

Help?!