If you have a scheduled outage with Salesforce in which Salesforce is 'Completely unavailable' what error message does a client of the APIs see when someone tries to call it?
Is it a login failure? A 500 server error?
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For scheduled outages, it is usually a 503/Server Unavailable
However, those can also happen for unscheduled outages (that, or a 500/Internal Server Error)
We've run both apps against the SOAP API for years, and some more recent apps against the REST API (Apex REST). I don't recall ever seeing a different error code.
Additionally, you should code for timeout errors like Atul suggested since when Salesforce is having a bad day ("performance degradation"), the requests will probably never return at all.