Are any restrictions set on the devices? access to the app store and accounts must be enabled in order for the invitation to be accepted on a device.
We manage 500 iPads and went through a huge phase trying to get this to work. There are a lot of specifics involved even down to the order you do things in.
We used to have all devices in groups, but VPP just didn't seem to work with that.
We now create a separate "User" and have say 20 iPads under that user and push VPP apps to the user rather than to a group or individual device.
You only need to accept the invitation once and one device per user. We do not use groups.
When you send an invite to a device from the server, you should get a prompt from said device which should ask whether app and book assignment should be allowed. Upon accepting that, it will take you to the app store and ask you to sign in with an itunes account. after you are signed in, any device enrolled within that user will now have the ability to receive VPP App pushes.
Once a user is enrolled, you can re-enable all restrictions.