With friends : No apology required

With professional friends : Usually a follow up chat not pertaining to the apology or topic at hand

With lovers : Usually a hug is better than an apology.Else use the universal apology ‘I love you babes!’

In your case, one apology is apt. Girls are sensible enough.Even after that if she is not coming back to her senses,you are sensible enough to let her go!

PS : Those who want to come back do come back.More apologies make it worse and not better.

Source: What should be done after apologizing?