Yes, I have a Windows 7 32-bit virtual machine running on my desktop, and I was able to use vBackup on that machine to successfully backup virtual machines from on the ESXi testing server. I tried using that same installation of vBackup on the Windows 7 32-bit machine to connect to the production server and perform backups, but I still get the same error message, identical to the one from my first post.
I have just now tested this to confirm, and the same Windows 7 installation of vBackup is still able to successfully backup virtual machines on the testing server without any issue, even after failing to backup VMs on the production server.
Thanks again for all your help.