I think there would be a chance of them going at it again. In a scenario say the two are hanging out in the same vicinity with several friends around, the topic comes up as to who would win a fight or who is stronger . Then someone says y’all settle it right now by arm wrestling. Not wanting to seem afraid of losing to the other they sit down and settle who’s stronger? Afterwards the winning girl is swamped with congratulations by many of those who watched it. Seeing the embarrassment since losing to her rival she needs to save face. All those watching only know what they just saw. Saying then she had to have won the fight too since she’s proven stronger. No way can she let everyone go on think it’s true she’s easily goaded into showing them they’re wrong. Which also forces the other girl to accept the fight or seen as being afraid she would lose.
