Lately, the problem seems to be bothering my daughter more and more. In most ways she is quite mature for her age -- it just seems that making friends is difficult for her. She's not painfully shy--she willingly talks to people. How can I help her?
Your daughter may not be "painfully shy" but she might be less socially mature than other kids her age. Perhaps she could ask a classmate who she thinks is nice to play after school at your house. If that's a bit too intimate for her, how about your taking her and a classmate of her choosing to a movie, bowling, or out to lunch? She needs to break the ice and you could rehearse with her how to approach a classmate and ask her to play with her.
I'd also return again to seeking out social situations for her outside of her school. Does she have any interest in drama, 4-H, or scouting? Brainstorm with her and come up with kids' organizations that she might be interested in. She might make friendships while volunteering with other kids at a local food bank or charitable organization. You need to help her expand her social universe. In so doing, you'll increase her chances to meet new kids and make friendships. Give these suggestions a try and write me back on her progress.