When someone cuts a friendship off, advice?

I met a friend at work and we have got to know each other the past two years. Anyhow,there's some other work colleague who for whatever reason got jealous of our friendship so started spreading rumors to my so called friend. My friend stopped talking to me for a week but eventually came and explained why because of this so called rumor that I date guys and drop them,I asked him why he stopped talking to me because of this and why is he bothered anyway because we're only friends. Eventually I forgave him,then today out the blue he said he wants to cut our friendship off and he mentioned the rumor again,I'm angry that I gave him a second chance just to cut me off again. Should I confront the woman who spreading lies about me or just let it go so I don't cause drama at work?