Low scale inflation has many virtues and it has been claimed that its natural realisation in supersymmetric standard model can be achieved rather easily. In this letter we have demonstrated that also in this case the dynamics of the hidden sector res
ponsible for supersymmetry breakdown and the structure of the soft terms affects significantly, and in fact often spoils, the would-be inflationary dynamics. Also, we point out that the issue if the cosmological constant cancellation in the post-inflationary vacuum strongly affects supersymmetric inflation. It is important to note the crucial difference between freezing of the modulus and actually stabilising it - the first approach misses parts of the scalar potential which turn out to be relevant for inflation. We argue, that it is more likely that the low scale supersymmetric inflation occurs at a critical point at the origin in the field space than at an inflection point away from the origin, as the necessary fine-tuning in the second case is typically larger.
