  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 responsible 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.
