Do you keep regular backups?

Answer

1.  This is just a way to tell how serious they are about the safety of your data. If they're not hosting your system, this is actually not their responsibility. Despite that fact, they should be keeping backups of everything they touch.
2. Yes, we have automated backups running for your database (most important), code, files and server at least once a day (hourly is better). This is the answer you want. Less than once a day (unless nothing is happening on the system during that day) means the impact of a crash or a mistake could cost you days of work and data. Any longer than this shows an amount of negligence. Keep in mind that depending on your relationship with them, they may not be capable of performing all of these backups.
3. No. or We backup manually every so often. This is more common than you'd think. Mistakes happen, systems fail: and it often happens when you're least expecting it. This demonstrates a lack of experience or plain negligence.