When a friend of mine got hit by the 1and1 email nightmare the other week I set up a secondary forwarding of his email (his DNS/MX is handled by 1and1 but they had no problems in that department at least!

) to a new gmail account I created for him. So even though messages were taking hours to reach his 1and1 mailbox (and hence his PC) he could view them instantly using the gmail webmail interface.
I'm not saying gmail is necessarily the best "backup mailbox" solution for you but if you want to ensure your customers' email doesn't suffer extended downtime then I guess the trick is to build in redundancy at every stage - i.e. not just MX but also mailboxes as well.
If your domain registrar gives you sufficient control over DNS then you can also reduce the TTL of some/all of the records so that any changes you might want to make propagate more quickly ... maybe this is a bit naughty, not sure ...

but the BBC do it (TTL of their A records appears to be 300s)
_________________
http://www.alexoria.co.uk • Increasing the value derived from information technology