Bhagavad Gita

ಭಯಾದ್ ರಣಾದುಪರತಂ ಮಂಸ್ಯಂತೇ ತ್ವಾಂ ಮಹಾರಥಾಃ ।
ಯೇಷಾಂ ಚ ತ್ವಂ ಬಹುಮತೋ ಭೂತ್ವಾ ಯಾಸ್ಯಸಿ ಲಾಘವಮ್ ॥೩೫॥
bhayād raṇāduparataṃ maṃsyaṃte tvāṃ mahārathāḥ |
yeṣāṃ ca tvaṃ bahumato bhūtvā yāsyasi lāghavam ||35||

Gist of the sloka:
Others consider you has a great fearsome warrior. Once you withdraw the same people will consider you as a coward, as a person who could not face them. They will laugh at you.
Perception is as much important as reputation. Arjuna having fought so many battles had a reputation as a fearsome warrior who is difficult to face and to survive to win. With that being the reputation, the other warriors would already have in their mind, great fear to face Arjuna. In case he withdraws, the same warriors would now mock him and the perception [that he was a fearsome warrior] that he had accumulated over so many battles would be forever be erased.