How stable is using a Custom Domain with office 365

Hi

I am using a custome domain in office 365 Plan E1 and  my concern is to know how safe security wise and how stable it is to use a custome domain? if the custom domain that we linked to office 365 e.g Contoso.com  is down how does this affect our office 365 features like Sharepoint, outlook etc that are liked to this domain? are there any articles that explain more on this matter and is there a way to prevent such crashes form happening e.g by configuring or using specific settings in office 365?

Thanks