Don't stir the yogurt! Stirring breaks it up and leaves it very unappealing. In my cheesemaking classes, I share a gallon jar of homemade yogurt and have to ask that the students not stir it. I'm not sure why people want to do that, but homemade doesn't have the stabilizers and thickeners that storebought yogurt has, so it can't stand up to that treatment.
If that isn't your problem, leave the milk sitting for 20 to 30 minutes before cooling it down, or simply allow it to cool at room temperature before inoculating it. It does take some time for the proteins to stabilize.