Brad,
That is indeed very strange, but I can imagine that broadband noise caused by static electricity could be one factor in this specific case. I have seen this before (not in emulators, but in other systems).
However, the fact the emulator is reporting a power failure on the target may be indicative of a faulty TVRef sense line (pin 5 of the JTAG connector, as shown here). The reason is that this line does not carry signaling but a steady VCC level throughout the debug session. In this case, I wonder if adding some bypass caps to pin 5 on the board could help mitigate this effect.
Unfortunately this seems to be a spurious combination of factors that include the lab environment, the emulator and the board circuitry, therefore the different hardware between the XDS200 and the XDS560v2 can be enough to suppress this effect (filtering or cable / trace lengths, for example). Hopefully a minimal difference can enable the XDS200 from Blackhawk to properly work under the same conditions (both manufacturers share the same basic reference design). Please report back any findings with this respect.
For a similar effect captured in an oscilloscope, you can take a look at a three-part series on this video blog.
Regards,
Rafael