I may have figured out what the problem is. I spoke with one of our network engineers and he mentioned that the DSN for the Pervasive database relies on a mapped drive location. The agent does not load a profile when it runs, so the drive mapping is not executed first and the DSN connection fails. When I ran it from BIDS, SSIS and command line DTEXEC, it was all running under my profile so the drive mapping was established.
I'm going to work with him later this week on a possible solution. I'll report back then.