When it comes to hours of work (in particular with support), you need to balance things between a best endeavours type issue, or an actual problem and of course the severity of that problem.
You should use your own judgement and common sense.
Work a normal day (8 hours) and maybe do the odd evening shift, but have a decent text or e-mail alerts system say things do go wrong in unsociable hours. Therefore you are kept alerted of the problems.
There are definitely going to be times when you're up until the early hours of the morning with certain issues, but there is no reason for you to be killing yourself doing it day-after-day. You just need to organise yourself correctly, that's all.