Thank you for your response, Pupul.
Yes, I was logged in to the server that was being updated and opened Task Manager to see if the system updates were being executed. It was and my assumption that the updates were completed successfully. What I don't understand is why OME is not able to connect to the server (and the system update task to state that it completed successfully) even though I am logged in to the server (to ensure that it was still up and running).
There were a few times in which I have executed system updates (which failed according to OME) (and which needed to reboot since there was a lot of updates taking place like BIOS, etc) and even though I ran and reran inventory updates numerous times, it looked as though it installed a few updates and I've had to create another system update task to finish the rest. Is that normal?