Hunh...well this is interesting. It looks like the problem is caused when a project uses lots of RAM and there is more than one instance of AT7. I've replicated it with just a couple of synths that use a total of about 13GB of RAM. Once that happens, if I add a couple tracks of AT7 I get the blank screen.
The fun part, though, is this: I'm one of the folks around here that uses more than one DAW in my joint. For kicks I thought I'd see if I could replicate the behavior on other DAW's, and sure enough, the same thing happens in Reaper 4.55 and Cubase 7, in fact, in those hosts it just outright crashes the DAW. Haven't tried in PT yet, but since it's not a VST in PT it's probably not apples-to-apples.
Anyway, sounds like I'm off to contact Antares support. Figured I'd post this for posterity.
Dean