...whether Saito from Gifu was correct, I cannot guess.
I finally got the word from my wife, who is from Nagano and teaches Japanese elementary students on Saturdays.
She said that makeru means to lose, but mairu means to admit that one has lost. So the correct form of the term we're discussing, according to her, is maitta.
Saito was a good guy, but he wasn't a linguist and maybe I misunderstood.