Can't update Sync 3. Message: Installation paused

I think you might have an issue with the APIM. Here are 2 threads that illustrate the same issue, the resolution was to replace the APIM.

Installation Paused…USB Has Been changed - Ford / Sync 3 - CyanLabs Official Community

Sync 3 Upgrade Failing - Ford / Sync 3 - CyanLabs Official Community