My $0.02 is that if you charge your clients as part of an overall hosting solution, then you either have a rate card or a monthly rate that covers issues such as this.
Else, it's outside of your usual work, then it would be reasonable to bill for your time.
I think you're right - I not sure how to broach the subject with the client though. tyvm for your $0.02 :)
However, you might want to use this as a opening point for discussion with your client should something similar happen in the future. It is your responsibility to set expectations but if the client merely expects you to work for free, I would say then you know what you need to do...