... Bring it to the mods' attention. Don't take on the user multiple times.
We've had a few separate instances over the last couple of months where higher-reputation users have actively (or passively) challenged newer users' behaviour repeated times. In comments. On Meta.
These challengers only do it for the betterment of the site.
However, leaving more than a few comments against a single user —especially a new user— makes them feel abused. They get defensive and their reaction is automatically against you, not the rules of the site, not their problems. Words like "troll" come up and that often just leads to another reaction.
Consider it this way. If they ignored you the first two times, what's special about the next ten? Continuing to nibble at a repeat offender will only make them angry. It won't fix the problem.
So, please don't nibble.
If you notice that a user is becoming a repeat offender, flag something they've done and leave an explanation for moderators. We can have a discussion with the user out of public view with them. Why?
- Well, sometimes the setting and person talking to them can make the difference and improve their conduct (win!).
- But sometimes they just attack us instead. The difference here is we can deal with that escalation surgically without a public brawl.
Either way the outcome is cleaner. You can focus on what you were doing, we can focus on the bigger problems and everybody stays calm and productive.