Inspired by a twitter conversation, I wrote an Instagram backup tool. It's a command-line tool. It'll store your auth token locally so you can run it unattended after the first run. It'll download incrementally, so you can cron it nightly.
Other backup tools for Instagram exist, and I really don't care, it's a 20 minute hack. The authentication step is a little weird (does OAuth2 really not have a pure desktop app flow?) but bearable. And it works for me. Let me know if it works for you.