Is clique-width preserved under edge contractions? Let $G$ be class of graphs with bounded clique-width. In each graph in $G$ some edges are contracted (e.g. randomly). Is now the clique-width still bounded?

In case it is (in general) no longer bounded, I would be very interested in a counter-example.
This recent paper finally proves that edge contractions do not preserve the property that a set of graphs has bounded 
clique-width.