It depends if you are direct or indirect. Because by walking with her/chasing her you are lowering your value(quite a lot). So if you are indirect it doesn't matter that much. In fact if you are indirect by chasing her you may save the approach. If you are direct then going after her is the stupidest thing you can do. Just accept that you screwed your approach and move on(remember she's not rejecting you but your approach).
Note about the continuing to talk - she'll may feel that she's not being polite leaving you like that and she may reconsider her behavior. So she can stop(quite possible) and even come back to you(possible but don't count on that). If she stops you can slowly go to normal talking distance as before.
If you'd watch it as a third person, who woul'd look more confident: the guy who is standing his ground or the guy who is chasing the girl like a puppy?
So you are right. Sometimes it's good to chase her. I wouldn't do it even if I'll go indirect but that's my point of view on things.
As I've mentioned if she doesn't stop or even slow but gives you a smile go and reopen => see those Sasha videos.
If she doesn't stop and keeps walking => your approach is bad. Change something.
PS: the walking/chasing thing can be seen on this guy's videos http://www.youtube.com/user/urbanistgame/videos
In most of he's approaches the girl slows down but keeps walking and he start walking next to her and it leads to no where.
We are different each one of us and some things work for someone but doeasn't work for another one. The golden rule here is: if something doeasn't work change something.