It looks like I finally have it figured out. Even though my super user shows to be a Domain Admin and the Domain Admins had full rights to the Destination folder, after I explicitly gave full access rights to my user it started working. Since the original user that it was set up to use was no longer working, I have to assume that one of the server guys changes the permissions for that user. I also suspect that you have to close the DP Studio before the scheduler can run a job but I will test that later to verify it.

One thing that I noticed is that if I make any updates in DataPump, when it refreshes the Scheduler it checks the "Do not store password" checkbox which can only be set in the Scheduler. I have to close DP and manually reset that flag in order for it to stick.