Thanks for the suggestion about VMWare, but my group is not responsible for the VMWare infrastructure. Basically we've been told to work around the issue from management.
With that in mind we did some more searching and found a system event of fixing the clock on the system. So we believe that something in the snapshotting process caused the clock to need adjustment. Thus this caused the issue with the task failing to start. Still thought it was interesting the symptom of the task thinking it is still running when it is not. But, with the idea of needing to adjust the system clock to duplicate we tried a few tweaks with the scheduled task the options “Stop the existing instance” and “Run task as soon as possible after a scheduled start is missed”. Initial tests have been successful but time will tell.
Last remaining trick is to see if the vendor will support our change.