Yes it got old for me too (fairy recently). I think going back & forth for a few rounds ain't bad, but after you feel like you've clarified the main points that you wanted to clarify (in case the person may not have heard your angle before) it's probably best to let it go.
I think the goal is to have the wisdom in recognizing 2 groups of people, as opposed to people who just want an argument...group 1 are Christians sincerely damaged by objections to their beliefs (maybe even recently threw in the towel), and group 2 are sincere seekers. In both groups the key word is 'Sincere.'
SOMETIMES, very rarely, you have that story where the die hard, arrogant, condescending skeptic who loves to argue gets converted. Let's call that person group 3. I think where most people get themselves in trouble (starting with myself) is that they constantly tell themselves "This guy/girl might be a group 3!! If I could just..." I really want to put an end to that mentality for myself, it's too exhausting! I'll do a few rounds with group 3s, other than that just group 1 and 2 for me if I could help it.