I've verified that the system time on both are exactly in sync within one second or less. Also, there is no pausing of the jobs at an any time, the job history shows they're running every 15 minutes (default config) 24/7 with no failures.

This is a perplexing issue, I've looked at all the seemingly obvious stuff, and there is nothing that points to why SQL Server is reporting sync errors. It is like there is an invisible history table these jobs are talking to and reporting on that is incorrect.