Wait, this is news to me - which VPS providers do not have persistent data storage? Are you thinking of Heroku-like deployments? I feel like every VPS provider I've encountered always listed storage as a feature?
I was thinking about EC2's default instance storage - it's ephemeral and gets wiped when you restart or stop the instance. Without paying for EBS volumes, EC2's storage is non-persistent by design.
You can't rely on VPS disk - backups, data retention and recovery is all up to you in case of node failure. There are other much more expensive and much slower products (external networked volumes) that do offer guarantees, but that's additional charge.
Well, Amazon might fail as a company at some point and then all your data will be gone. Theoretically.
Much more likely, though, is that you, or some sysadmin at your company, or even some user will accidentally hit the "delete" button on something important, and then without a backup, you can't get it back. Which is honestly the thing that people usually need their backups for, anyway. This is what most "data loss incidents" are: people just messing up and deleting things they shouldn't have. Wetware is much more prone to failure than hardware, after all.
Yes, and you never use those, because if the VPS company fails, your backups are gone. So use the backup services of a second (and third) company if you value your data.