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Fractal dimension (FD) has been considered as a potential biomarker for retina-based disease detection. However, conflicting findings can be found in the reported literature regarding the association of the biomarker with diseases. This motivates us to examine the stability of the FD on different (1) vessel segmentations obtained from human observers,(2) automatic segmentation methods,(3) threshold values, and (4) region-of-interests. Our experiments show that the corresponding relative errors with respect to reference ones, computed per patient, are generally higher than the relative standard deviation of the reference values themselves (among all patients). The conclusion of this paper is that we cannot fully rely on the studied FD values, and thus do not recommend their use in quantitative clinical applications.