While trying to access to ListData.svc service in a SharePoint 2010 sub site I was getting authentication prompt to enter credentials again and again. I was using a SharePoint Farm administrator account so was sure that permission is not the cause of this problem. So I started SharePoint Manager, browsed to the sub site and saw that there was a problem in a feature
Afterwards I checked in the list nodes of the same site to see which lists were included in this missing feature, after clicking on one of the lists I got the following error which hinted that this list was the one included in the feature.
Further in the properties window there was an error message in the content type field
I deleted this orphaned lists and the service worked fine then.
I hope you found this post helpful. Thanks