vCenter being non-operational left me a bit of a doom and gloom feeling but, thankfully, the fix is rather easy.
Fixing the issue
Open up an SSH session to your vCenter server and run the command below to remove the software_update_state.conf file.
You can check the contents of the file by opening it with vi, an example is shown below.
Turns out that the state “INSTALL_FAILED” is checked by the python script that performs the installation. The script can be found in /usr/lib/applmgmt/update/py/vmware/appliance/update/update_state.py
Removing the file will make this check pass and the installation will continue.