Thanks a lot Stefano and Byte. I'm most grateful for your help in getting this fixed. Removing the affa backup files has sorted out the issue. The emails are now flowing and the users are more than glad to be back online.
I'll uninstall the affa for now; even though there are currently no active jobs scheduled. I'll also keep an eye out for the trend in the usage of the remaining storage, just to be sure that there's nothing else running out the disk space.
Will definitely endeavor to improve my SME skillset. Who knows, I can be of help to someone else tomorrow!