Uh, yes they do. You want a unit or system test which covers the case where an external system is down or returns something that you can't parse. Something like:
# code to take third party thing down
# eg. mock out lib and return nonsense (unit tests)
# or add an /etc/hosts entry (system tests)
assert "Sorry, but that feature is unavailable." in page.content
Now the entire app doesn't asplode, and you can wait until 9am to fix it. Follow up is to make sure that you're on whatever mailing list tells you when changes are coming.The only case that this doesn't cover is when it's a) an essential part of your app, which b) you aren't paying for and c) they don't have a mailing list, in which case wtf? you need to find a better 3rd party library/service.
ps. Look up the "chaos monkey" - it's very enlightening :)