What should I do about my colleague who avoids me despite my repeated attempts to reconcile with her and appease her, and am I sinful if I stop greeting her due to her continuous rejection?

You did well in apologizing to your friend, and you have fulfilled your duty. We advise you to do everything in your power to mend what has been broken between you. This includes supplicating to Allah to reconcile between you, and involving trustworthy sisters to mediate and remind your friend of the virtue of forgiveness and the consequence of abandonment. If reconciliation attempts are unsuccessful, there is no blame upon you. As for initiating the greeting of peace (salam), it is a Sunnah, and returning it is obligatory.