HERE are some general tips for tracking down Audio issues in PrPro. Perhaps there is just a setting that needs adjusting.
As you have Audio in one Monitor, but not another, I rather doubt that the issue is with a setting, but it will not hurt to look.
Usually, Audio issues are just the opposite, of what you describe - Clips play fine in the Source Monitor, but not in the Program Monitor. The Source Monitor is accessing the actual AV file on your HDD, while the Program Monitor is accessing the Timeline and the CFA files for Audio, and there is a difference.
Good luck, and I hope that others have more useful ideas.