The TPR*-tree is the most widely-used index structure for effectively predicting the future positions of moving objects. The TPR*-tree, however, has the problem that both of the dead space in a bounding region and the overlap among bounding regions become larger as the prediction time point in the future gets farther. This makes more nodes within the TPR*-tree accessed in query processing time, which incurs serious performance degradation. In this paper, we examine the performance problem quantitatively via a series of experiments. First, we show how much the performance deteriorates as a prediction time point gets farther from the present, and also show how the frequent updates of positions of moving objects alleviate this problem. Our contribution would help provide important clues to devise strategies improving the performance of TPR*-trees further.