Hi Jeff,
I would check the payload traces in transaction SRT_UTIL and see, whether there is any difference between the requests sent by SAP. Look for the HTTP Header, there should be Basic authentication data there (Base64 encoded). If it's identical (most likely), the provider rejects this with 401 for no known reason by SAP. Ideas: user gets locked by someone else at the same time, or for other reasons, they need to figure this out.
If you don't see in those requests the auth. data in the HTTP Header, check if you used the same Logical Port for the call.
Also, check the Troubleshooting Guide for ABAP WS, it helps you find the root cause (how to trace, analyze traces, common problems, etc.): Troubleshooting Guide - Web Services ABAP - ABAP Connectivity - SCN Wiki
Cheers,
Attia