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If emails are a part of your core business, you should have a business continuity plan for this situation. That may be to fall back to another service, or even a temporary in-house server.

Of course, if it's that important, then you'd be foolish to not have invested in a better solution, or to not have a proper SLA with a third party.

That's why you always set up a local mail server that delivers onwards to these services. I documented how to do that with Haraka here: https://baudehlo.com/2016/07/26/setting-up-haraka-to-send-to...

This is a major risk of outsourcing part of your operations. You probably shouldn't do this to the core of your business, as you lose control over problems. But sending marketing e-mails usually is not the core of business, unless one is selling the service of sending e-mails.