I am getting ready for an annual puppet show at a local "Baby Fair." The audience is not captive, as I just entertain kids in an open area while their parents roam and look at the vendors. The audience is made of kids from infants to 7-8 year-olds with some parents and is never more than 10 or so kids in size. I have an extremely hard time getting the kids to respond to me in any way, so the performance ends up flat. Any advice on the matter would be greatly appreciated.

I know how this feels. You'll need to involve them with audience participation. I don't know your act and your skill level, but magicians will bring a kid up and use them in their trick, hold the wand etc. Vents will bring a volunteer up and use them as the "dummy". Audience participation is a must. Kids love to watch other kids in situations like this. Also, use a warm up to get them clapping and laughing. Here one that works well. Hold your hands out and say you are going to have a contest between the boys and the girls (or this side and that side)to see who can clap the loudest. When I raise this hand, this group is going to clap....when I raise THIS hand, THIS group will clap. Work them back and forth trying to figure it out, finally raise both hands for thuderous applause and take a cheeky bow....thank you, thank you!

I recommend that you put down a blanket for a sitting area. This particular group becomes your audience and you focus toward them and any standing directly behind them.
Have a revolving show and a sign that says that. (This is a 20 minute show that on the hour and half hour.) Use the 10 minutes between tow pass out cards, answer questions with a puppet, or ask what their favorite was.
Start with something that you can stand to have interuppted with new people coming in. Don't start a ten minute story that people won't understand who came in late. Perhaps magic to music would be a good opening.
Make your audience loud: ("Oh, dear, I can't wake my lion up! They sleep 20 hours a day, you know! Just like a teenager! I think we're going to have to wake him up. Let's count to 3 and yell, Wake up, Leo!")
"Let's practice the Hollywood laugh: When actors film a movie sometimes they have to laugh and sometimes they have to cry. They learn different types of laughter... There is the one Ha laugh. HA! (2) HA, HA! Three (HA<HA<HA!) (4 and 5). Today's show is rated 3 laughs. I want you to laugh out loud as often as you like, but only 3 laughs! Then my funny friends will have time to tell more stories! Let's practise a 3 ha Hollywood laugh! My what great actors you are!