As you pointed out, this is likely an issue with the proxy setup in your environment. Specifically, I believe this is related to proxy authentication. I know you said that the 3 computers are all configured the same, but if they were exactly the same then they would behave the same. They are not behaving the same, so therefore there must be something different about one of them.
Please review the instructions:
'Scenario 2: The Windows Update Agent on target computers is properly configured to use the corporate proxy, but the proxy requires authentication'
Using BatchPatch with an Enterprise Web Proxy
-Doug