Try running it straight into the DAC without the Monarchy.
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Is the problem only with internet radio or does it also happen when you play stored files from your computer?
Have you tried using the Duet's analog outputs (without using the external DAC)?
Does the external DAC work OK with other sources?
If everything works fine separately, then I'd take a good look at the interconnect between the Duet and DAC.
The Slimdevices forum is also a great source of info since it is obviously focused on their products. Check it out at http://forums.slimdevices.com