In 1982 Bobylev [A.V. Bobylev, Sov. Phys. Dokl. 27, 29 (1982)] made a linear stability analysis of the Burnett equations and showed that beyond a certain critical reduced wave number there exist normal modes that grow exponentially, concluding that the Burnett equations are linearly unstable. We have partially extended his analysis, originally made for Maxwellian molecules, for any interaction potential and argue that his results can be reinterpreted as to give a bound for the Knudsen number above which the Burnett equations are not valid.