Here are my testing results:
First, I have trouble just to have the VXI driver loaded into the system when logged in as a restricted user. In MAX, I will see a black cross mark(not red) and "run resman" is grayed out as a result of no driver loaded.
Second, I tested the same hardware setup with NI-VXI 3.3.1 and resman could be run fine under the restricted user account, I am remember correctly, you haven't tried upgrade your driver yet. this could be the easiest solution to this issue.
Also, it looked like you have Windows2000 or XP instead of NT, or am I mistaking?
Finally, please let me know step by step on how you set up your hardware, software and restricted user account. Apparently we have seen different behaviors when logged in as a restricted user and at least you could load NI-VXI 3.2 correctly.