[Mark McLeod]

Don't know why Run would inhibit the User Watchdog (but I'd suggest not letting it distract you from fixing the obvious Watchdog problem, of course).

The message you see is generated from the User watchdog and the operation of that is self-contained within your code running on the cRIO. It doesn't depend on the Classmate for anything. So Run would have to be affecting the execution of the Watchdog delay on the cRIO somehow. That's implemented below the visible layer of code in the FPGA, so the FPGA programming might be smart enough to allow for slower response times when LabVIEW is running in debug mode. Joe Hershberger would be the one to know.

The Classmate doesn't affect the User watchdog, power-saving or no. The fastest PC you have won't matter to the User Watchdog, because that's not what it's watching.
The User Watchdog is concerned solely with how often your cRIO code feeds it. Sort of like my neighbors cat. It doesn't care how it's fed or who feeds it as long as the food shows up in the bowl at regular intervals.
A laggy Classmate might affect the System watchdog, but that one typically just shows up as a count on a Diagnostic tab message, or as jerky robot motion, not as "Watchdog not fed".