I've never used them for large volume actually. Are you using them via SMTP or API? I'm asking because I've never seen a single API call fail with them, but maybe it's about the volume like you said.
For large volume sending, I'd probably use AWS SES. In the past, I've used it for sending 150-200K/transactional emails per day and the service was very robust.
On the other hand, I've seen Mandrill increase the number of failed API calls with a lower sending volume.
It still does not support multiple admin roles per account.