That is a good question. For years I somehow didn't trust Dreamhost to renew my registrations automatically, so I always renewed them well in advance. One time, I decided to actually test my intuition, so I set a less-important domain to automatic renewal and waited to see what would happen.
Can you believe, it went past expiration without being renewed.
Here is the message I sent to support:
and here is the response,
Shortly after that I moved all my registrations away from Dreamhost (except for the one "free" one of course). As I am still a Dreamhost customer (their hosting has good points) I hope that we can press them for a better answer about auto-renewal than the inadequate answer which they gave to me (quoted here).