Since I currently don't have a Mountain Lion install on my Mac Pro having upgraded my primary OS to Mavericks (but finding performance on certain very important applications abysmal and subsequently reported as a bug), I booted into my older 10.7 Lion (I regularly sync all my data to this partition as part of my backup strategy), added my Yahoo account (when I was using this OS version exclusively, Apple had not yet incorporated an easy option to add a Yahoo account to Mail, or I just never noticed that option) and have not had a single, dreaded connection issue to Yahoo e-mail thus far (knock on wood), with nothing else being changed on my iPad and iPhone (both setup to access the same Yahoo account).
So could it be something to do with Mountain Lion and/or Mountain Lion Mail (whether it's a Yahoo and/or Apple compatibility issue)?
I miss the full iCloud integration of Safari with 10.8+ so eventually I will go back to one of the newer OS's. But for the time being, I'm enjoying unfettered access to my Yahoo (standard) account through mail on 10.7 Lion.