> What if you don't have access to your server for a week?

Then you've chosen a bad service provider(s) to host/colocate/peer with.

Actually, you should notice this situation pretty much immediately you're online - because most likely your IMAP server would be down - and every single email client I've used had started to display warnings.

If you have more complex setup with separate MTA so your IMAPd may be online while your STMP service's unreachable, then you should set up monitoring system and deliver alerts either using local delivery or any out-of-band mechanisms (like SMS).

Also, you can set up a backup MX. Or two. Or more. Email has failover/HA since forever.