They workout the issues like everyone else, and at a certain size the issue is minimized as you are either in several whitelists or human moderators recognise your domain.
Most of those services also let clients setup their own domain name, so a ban is a more of a inconvenience to deal, than business critical like in OP case.
Most of those services also let clients setup their own domain name, so a ban is a more of a inconvenience to deal, than business critical like in OP case.