Permanently install a non App Store app on an iPad - without expiration
No, it is not possible. All current methods of distribution, including those available through the ordinary App Store developer program and the Enterprise Developer program, have expiration dates.

Another answer mention Enterprise distribution as the solution - but it is not. The provisioning profile expires after 1 year, and the certificate itself after 3 years. So you would have to renew it in order to have the app working for many years.