In the situation Roberto describes above it is not necessarily just the Mendix application that is updated, it's also other external components Mendix relies on (external app-servers, services, etc). If these are being upgraded the portal may have to go offline momentarily as well (and this duration is typically longer than the Mendix upgrade).
My thoughts would be to
 Temporarily deploy a different Mendix-application that just presents a Maintenance page, or
 Switch the Mendix-application to a Maintenance page (prior or after being upgraded itself), preferably based on an external trigger (i.e. the deployment processes/scripts that upgrade the external components that Mendix relies on).
 Alternatively, we need to front the Mendix business server with an Apache webserver, redirecting to a Maintenance page.
The last option  is certainly doable, I am less sure about the ease of implementing  or .
Am interested to hear your further thoughts!
Good question. May be you can handle the 'service not available' error and display an alternative page. This would be great locally as well. How often have we pressed F5 because the runtime was not ready, but got no answer but a blank screen?