It is well known that a wide range of impulse control problems are continuous, but not differentiable, with respect to intervention cost as it approaches zero. We show a similar non-C1 result, assuming that the problem and the value function are sufficiently nice. The result is that if the value function is locally C1 in the state variable, then it does not admit first order approximation in the intervention cost. Our analysis also covers problems with reflection (i.e. vanishing impulse).