While I should warn that it's probably something to do with your mailbox store, to answer your question:
Under Mail/Preferences…/Accounts tab you'll see incoming and outgoing mail server names. Sometimes those names point at physical hardware instead of aliases given to you by a name server. Think of the mail service not as a computer but as a virtual entity that can be pointed to anywhere, even if temporarily. If the server hardware changes a hard-coded server name won't follow the service it if it's not pointing at an alias.
I thought of this because you only lost incoming, not outgoing, a typical scenario for admins swapping server hardware as some don't distinguish between virtual services and hardware, you know, pointing the finger at the box and saying "that's the mail server", when the service and storage could actually be aliased to any equipment that's available. A good setup will point to an alias from day one, so that admins have future flexibility to evolve without interruption just by maintaining an accurate DNS.
Sorry if I've led you down the wrong path. Stalling a mailbox rebuild sounds like a different kind of problem.