This error may result if the server's IIS is configured for any port other than port 80. ACT! Internet Sync only supports port 80 at this time.
Error code 401 may also indicate that the remote computer (where the subscribe database resides) has not provided the proper Window's credentials to the web server hosting the Internet Synchronization Service. One way to mitigate this is to allow Microsoft Internet Information Services to accept anonymous incoming connections to the ActInternetSync virtual directory.
See the following document for details:
Title: How To Enable Anonymous Access on the ACT! Internet Sync Virtual Directory
Answer ID: How To Enable Anonymous Access on the ACT! Internet Sync Virtual Directory.