I have never known any bully to stop when being ignored- they certainly don't just say "oh they are ignoring me I will just stop"- NO WAY- they escalate it to worse bullying of the kid until it becomes physical!
I think the advice to "ignore" a bully is often not explained in a clear way. Sometimes it's even just a way for adults to shut the complainer (ie, victim) up and put the blame on them.
"Ignore" should not mean refusing to stick up for yourself, just taking the abuse without comment. If you do that, then yes - the bully will escalate.
A properly timed punch can be effective, it's true. But not all kids are going to be able to punch their opponents. Some because of draconian school rules, and others because they simply aren't physical fighters. I was one of those. Many, many people encouraged me to learn to punch. They had me practice making a fist and throwing my weak little punches at their hands. It didn't work. Punching is not my way of fighting.
Words, on the other hand! I'm good with my words. :-D
I believe ignoring a bully means not letting them provoke a hurt or angry reaction. "Ignore" is the strategic eye roll, the sigh of crushing contempt, the snarky comment that puts the bully in his or her place. Properly "ignoring" a bully is a skill that can be tough to master. It's the ability to convey both boredom and amusement at the bully's sadly ineffectual efforts to get your goat. It's an act, and when you've got it down, it's hugely effective. It gives the outward appearance of you taking the high road, while at the same time you're handily de-fanging your opponent.
I have "ignored" bullies of all ages, child and adult. I've done it on my behalf, and on the behalf of others. I remember in the Reserves, a young man was teasing a tiny Asian girl, curling up his lip at her every time she glanced their way. I got angry and the next time he looked our way I smiled at him and said sweetly (as if I was trying to be helpful), "Oh, no! Your intelligence is showing." His friends burst out laughing and he refused to look at us for the rest of the day. And after that, he was less of a jerk to her.
The problem is, we rarely explain this technique properly to kids and we almost never coach them in the skills required to pull it off. And sadly some kids will never be able to effectively master it - they wear their feelings out on their sleeve for everyone to see and exploit. They react impulsively. They can't pretend to feel something different from what they really feel. These kids are why we need to have strong adult leadership in schools, and effective anti-bullying initiatives among the students.