This paper focuses on asymptotic point-stabilization of smooth affine control systems. For asymptotic feedback stabilizers, a simple definition of {robustness} with respect to unmodeled dynamics is adopted. Two theorems are then proved which state sufficient conditions for the {non-robustness} of homogeneous stabilizers. The first theorem, which applies to systems that may contain a drift term, involves a specific class of feedback stabilizers. The second one, which applies to driftless systems and is stated independently of any particular stabilizer, provides a condition related to an eventual loss of rank of the accessibility distribution. One of the consequences of the second result is that, for {chained-form systems}, no (static) continuous homogeneous exponential stabilizer (some of which have been proposed in the literature) can be robust in the sense defined herein. Examples are provided which illustrate a typical application of each result.