We provided some apps for our students using the self-service option, however, we ran out of codes for one app, and thus some students were left with a "pending" notification when they went to the App Store.
We loaded more VPP licenses, and told the students to go back to self-service, but instead of downloading the app, for those who had tried before it is stuck on "pending" with no activity at all. Very frustrating!
Just guessing since I do not yet use VPP - but has the Pending app install for the student's device in History been Cancelled?
What I normally do for stuck app installs (In-House) is 1) try to delete the app icon on the iPad if it is there, 2) Cancel the Pending App, 3) restart the iPad, 4) Update Inventory.