Combine sugar, corn syrup, cinnamon oil and water in a heavy medium saucepan; bring to a boil over high heat, stirring occasionally to dissolve the sugar. Clip a candy thermometer to the pan and boil until the temperature reaches 300 degrees F and is at hard-crack stage (when a bit of syrup dropped into ice water is hard and brittle and does not stick to teeth). This will take about 10 minutes. Remove from the heat and stir in apple-juice concentrate. Return saucepan to high heat and cook, stirring, until thoroughly combined. Continue cooking, swirling the pan just until the mixture begins to color, 1 to 3 minutes. Immediately remove from heat and let stand until the bubbles subside, about 2 minutes.