What will happen if i increase the length of the string on a model plane?

I have a model airplane attached to a horizontal string, successfully maintaining flight in a 30' diameter circle. With all things remaining the same, i increase the length of the string to fly at a 60' diameter. Will the plane continue to fly? How about if I increase the string to a 120' diameter or even further? Is there some diameter where the plane will not be able to maintain flight. Does the diameter have anything to do with the planes ability to fly? For argument sake, the string weight has no influence and the prop speed remains the same at all distances.