My company isn't very big (we spend in the very low five-figures with Azure per month) and yet we were assigned an "Azure Success Manager" (or something close to that) who I have a standing monthly phone call with, and can reach out to at any time to oversee any issues that may come up. We actually did have a billing issue come up a while ago (it was Microsoft's fault) and although our account wasn't in any real danger of being shut off, she stayed on top of the case and made sure it got resolved quickly.