Since writing that piece, it has occurred to me it probably also means forgetting my manners.
The Deep South is very religious and famously polite as Ugly Americans go and religion and manners are seen as related in the Deep South.
So I think one meaning for the phrase is getting so upset with someone you fail to be polite and respectful as is generally expected from people where I come from.
You drop your Sunday Best behavior and go off on someone.