We have an On-Premises installation of SharePoint 2013, and some users with Windows XP/IE8/Office 2010. When these users try to edit an office document, they are prompted with an endless login. They will try and try and they will not be able to edit the document. If they Cancel out, they are able to open in the client application in Read Only mode. Users with other, newer Internet Explorer browsers have no problem.

It has been confirmed these people have contribute access to the library.

Is there a fix for this? Whats causing it..IE or Office?

Hi Rigamonk

Have a look at this article, which will help in fixing the issue:

SharePoint site continually prompting for passwords

Hope this helps you!