I decided to formally raise the issue with Stardock in case they weren't aware of the issue yet. They responded promptly, attributed it to UAC (doesn't quite make sense to me how that affects it, but I'll take their word for it) and suggested a work around which so far is working for me.
I've not yet tested the startup options yet, but I restarted multiplicity as administrator and it appears to have resolved it. I've not had any problem reproducing it before and am unable to do so now, so here's hoping it stays that way. I guess disabling UAC would also resolve it, but I've wanted to give UAC another go with Win 7 (so far it hasn't yet "annoyed" me like it did in Vista).
RESPONSE FROM STARDOCK:
This is a known conflict between Multiplicity and Vista's (Now Win 7's as well) User Account Control. If you run the multipl.exe file as administrator on any Vista machines (primary or secondaries) you should no longer see this issue. To do this:
-Navigate to C:\Program Files\Stardock\ThinkDesk\Multiplicity
-locate the file multipl.exe, right click and choose 'Properties'
-Click on the 'Compatibility' tab
-Under the Privileged level section at the bottom, check the box that says 'Run this program as administrator'
-Click 'Apply' then 'OK'
-Reboot the machine
This will flag Multiplicity at startup in UAC. You have a few options here, as unfortunately there is no way to whitelist the app in UAC.
A.) Every time the machine boots, right click on the blocked startup item tray icon and run Multiplicity manually every boot.
B.) Create a .bat file and add it to your startup items that launches multiplicity. You can simply copy and paste this line into a text file and rename it whatever.bat:
start /d "C:\Program Files\Stardock\ThinkDesk\Multiplicity" Multipl.exe
Once you create the .bat file, add it to the startup folder in your Start Menu.