Shared hosting ? If so ask your host if there's anything relevant in the logs, just tell them your site has stopped sending mail. Hopefully if they won't look at the logs they will provide them so you can see if there is some kind of clue as to the cause.
It is also (possible) they might of changed something at their end too which has caused this, but please take a moment to stop and think if you have made any changes at all (even something unrelated) lately to your community, perhaps a new addon or something along those lines.
Regarding access, well you are going to need it unless you want to wait for your host to reply (depends what they say , if its something they can fix aka: server config has changed etc) you could temporarily turn it off via adding this to your config file:
Code:
$config['enableTfa'] = false;
If/when you decide you might need to add that line, check its not already there (with true set), if so you simply need to change true to false. Not sure if you wanted that but thought you best have it so you know "how to" if you need to.
Hope that is a little helpp to start with.