Officially unless you remain in a chase (say within 10 k of the trader) from the first encounter, you should treat it as a second encounter.
As Bugs said above you can deal as much damage as you like (just dont kill him) before making a demand. That might be your course of action next time you meet.
I agree with Carzor, I'm one of those pirates who chases people to the edge of my ZOI if they simply try to get away, just to show them I'm serious and next time, they better pay.
If they get away after all, I'm less friendly on a next encounter, and I usually shoot at them first, and deal some serious damage, before i make demands. It's the most RP way IMO because a system jump shouldn't mean the pirate "forgets" about it all.
I have to admit though that I make a character judgement on the first pass based on his replies etc. and then make a decision how I react to him next time I see him.
If he's a Silent Bob I don't just bother chasing him too much. But if he sorta taunts me (in a RP way, not like lol stupid pirate) then I'm willing to go the extra mile really making an effort and make the game interesting to both of us.
One good tip which will I'll give you is pretty simple and spices up the things nicely. If someone got a lucky break and just whizzes by the TL. Then he uses open comms to warn about pirates in location xyz. I usually respond to this that "Thank you Mr. Squeler. You just upped your tax to double the usual. Next time you might want to mind your own business or perhaps use the private channels." Or something similar. I know that if he has any sense I probably won't be able to get him during the session, but it sure makes a nice follow on conversation.;)