This is a post to myself on how to fix this problem. The symptom is continuously getting the above alert from the WHS launchpad. The solution is linked here:

http://social.microsoft.com/Forums/en-US/3f1b6cd1-d1ef-41e2-8848-eb381f8df41c/continually-receive-alert-stating-one-or-more-services-are-not-running?forum=whs2011

From user Dowlo:

I think I have resolved this now. Windows Update service was set to Automatic (Trigger Start) on the alerting machine, and Manual (Trigger Start) on my other machines. I reset it to Manual on the problem machine and the alert has not resurfaced since.

A little counter-intuitive, but there you have it.