Why do *some* ScriptResource.axd requests fail on *some* computers?

We have a website that uses ASP.NET 4.

I have experienced the problem before where some ScriptResource.axd requests return 404 errors, but others succeed (on the same website!).

Now we have a strange issue where the above happens, but only on some computers. Other computers load the page without any issues whatsoever.

Clearing our browser cache seems to resolve the issue, but we don't want 开发者_运维知识库all our thousands of users to have to do the same.

Any thoughts?