We study the class of transitive skew products associated with iterated function systems of circle diffeomorphisms. We approximate any of those skew products by maps in this class with a robustly zero Lyapunov exponent. In particular, we prove the existence of non-hyperbolic ergodic measures for an open and dense subset of transitive skew products. Moreover, these measures have full support and are the weak
$^*$ limit of periodicmeasures.