Fig.: to lose credibility, credit or reputation

Many people are more afraid of losing face than losing money

Per molte persone è più grave perdere la faccia che perdere denaro

I'm sorry but I cannot do what you're asking me to: I don't want to lose face

Mi dispiace ma non posso fare quello che mi chiedi: perderei completamente la faccia davanti a tutti

Don't be such a show-off! If you make promises that you know you can't keep, you'll end up losing face and no one will trust you anymore.

Non fare il gradasso! Se prometti quello che sai di non poter mantenere, finirai col perdere la faccia e nessuno ti crederà più

Orientals in general and the Chinese (who invented this phrase and taught it to Europeans in about 1870) in particular, are usually willing to accept a defeat philosophically if the other side will make the tiniest move towards a compromise, so that it will save the face of both parties. Lose face is the translation of Chinese tiu lien