Thanks so much, Rosencrantz,
My head knows my children will work these things out, but my heart just aches. I know much of it is my own pain left over from my own losses on the playground. My husband is pretty supportive in that he tells me I'm doing a way better job of helping our kids than my parents did for me, just by listening.
BTW I don't step in and solve their problems, but I do want them to feel
OK 
even if a particular peer doesn't think so. Hopefully, home is a sanctuary for them. I tell them that there are some people who can only feel good when they are tearing someone else down. (There have been a few blatant examples in their school career so far). I encourage them to find people who accept them rather than bend over backward to please people who can never be pleased.
One identified bully was hammering my child for a long time. I finally said, don't give him what he wants. Don't cry. You can come home and cry here. Tell me how you feel. I guarantee you that if you stop crying, he'll find someone else to make him feel powerful. Let's give it a try. In this case, thankfully, it worked. Another parent had another method: he went up to this kid and said the next time you do that to my kid, I'm going to do it to your father. Nasty business.
Another hard part is that I am just now myself learning how to resist v. shrink way or disappear. I felt so unprotected emotionally while growing up. Unacknowledged. So I wonder if I am encouraging them to do something that I find difficult myself...anyway, finding the strategies for coping, surviving and winning are what's important. Thanks for the encouragement and for keeping me on track. Best, Seeker