I have a VMWare VM running off of a external hard drive. Works great and I have no problems with the set up. What keeps annoying me is that after about 20 minutes of inactivity the VM automatically saves its state and closes. Is there a way to keep the VM from becoming inactive? I couldn't find any obvious settings for this and it doesn't happen with my other VMs running off of a "regular" hard drive, so I'm thinking it could have something to do with the drive itself and not VMWare?
It certainly has nothing to do with the drive itself.
This is most likely caused by the power management settings inside the virtual machine: If your VM is set to suspend or hibernate after a certain idle period, it will trigger a VMware suspend.
Additionally, in your VM settings you have probably enabled the "Close after powering off or suspending" setting in the power options causing the virtual machine itself to close after such an event.