That sucks, arguments about veganism can emotionally draining. Changing minds is important, but make sure you look after yourself.
I just want to put one thing out there though. As someone who has been trying to convince everyone in their life to go vegan for some time now, I am continuously surprised at what kind of things stick in people's mind after a conversation. Even when you thought the conversation went horribly and had no effect on them. My Dad, who was brought up as a butcher, often asks me questions now about things that I said in passing during a veganism discussion months earlier. Just the other day, one of my good friends told me that she now hears my voice in the supermarket when she buys animal products.
None of this is to pat myself on the back, but to remind you not to get discouraged. Changing someones mind doesnt always happen overnight. I can almost guarantee that your friend thought about your conversation since, and that's half the goal, just to get people thinking.