It is mentioned in first page of [this][1] paper by Seiberg and Komargodski that the Lagrangian in superspace of a $U(1)$ gauge SUSY theory with FI terms is not gauge invariant. However, the FI terms in superspace is 
$$
\xi \int d^4  \theta V
$$ 
where $V$ is a vector superfield. Now if we do a gauge transformation on $V$, i.e.,
$$
V\longrightarrow V+ i (\Phi-\bar{\Phi})
$$ 
the FI term remains invariant since
$$
\int  d^4  \theta \Phi=\int  d^4  \theta \bar{\Phi}=0.
$$

So what is the source of the gauge non-invariance in superspace ?

  [1]: http://arxiv.org/abs/0904.1159