I took a look at the services running on the vCSA by running "service-control --status". It appears the VMware vSphere Profile-Driven Storage Service (vmware-sps) had stopped.
To get the service running, just run the following command: service-control --start vmware-sps
I was then able to successfully perform a storage vMotion.
Bonus info:
Here's a list of services running on the vsphere 6.X vCSA:
