This was a new one for me... logged into one of my Exchange 2010 servers, opened up the Exchange Management Shell, and got this:
Connecting to remote server failed with the following error message : The WS-Management service cannot process the request. The system load quota of 1000 requests per 2 seconds has been exceeded. Send future requests at a slower rate or raise the system quota. The next request from this user will not be approved for at least 1951063168 milliseconds. For more information, see the about_Remote_Troubleshooting Help topic.
+ CategoryInfo : OpenError: (System.Manageme....RemoteRunspace:RemoteRunspace) [], PSRemotingTransportExc
eption
+ FullyQualifiedErrorId : PSSessionOpenFailed
[h=2]
1 951 063 168 milliseconds = 22.5817496 days 
[/h]That's OK, I didn't really want to work on it anyway.

A reboot made the problem go away. I was going to blame the stupid throttling policy, but I'd already removed it.