Hi there,
I've experienced the same problem with IE8 in a https environment using a content editor web part - turns out the issue is not directly SharePoint as we was able to resolve it by disabling XMLHTTP support in IE8
Disable XMLHTTP support in IE by clicking on Tools -> Internet Options -> Advanced Tab -> Uncheck Enable Native XmlHttp Support.
Once you have done this restart IE
For more information see this:
http://social.msdn.microsoft.com/Forums/en-US/sharepointdevelopment/thread/b6e45b08-e042-4c49-819d-2b326f61f7a7 Hope this helps
Geoff