Store backups for a little while and charge a fee (high enough to make this service profitable) to release them.
A customer for 4 years and they delete everything after 5 weeks? Can you really defend that? It's pretty clearly a bad policy. You're being facetious about other contact methods, but I think that's a great idea. Allow users to add a phone number. Some people have faulty spam email blockers.
How should they get ahold of you? A call that you don't answer? A letter that goes unopened? African swallow laden with a note that you don't see?
Keep backups elsewhere. Regardless of cloud provider or payment terms or whatever. 3-2-1 backups.