Based on my semi-controlled observations, it seems that if I let my laptop go to sleep (as a result of being inactive with it), the target Vpp falls to about 3V when it's woken up again.
When I first boot the laptop and connect the ICD2, everything appears to be working okay, with the target Vpp around 10V. I think I'll try programming some chips, and see if I can find a way to keep the laptop from going into standby mode. I wouldn't mind doing that anyway, because it had a habit of going to sleep too quickly when not on the job. But what are you gonna do? It's a government computer!