  We are interested in the recursive model $(Y_n, \, n\ge 0)$ studied by
Collet, Eckmann, Glaser and Martin [9] and by Derrida and Retaux [12]. We prove
that at criticality, the probability ${\bf P}(Y_n>0)$ behaves like $n^{-2 +
o(1)}$ as $n$ goes to infinity; this gives a weaker confirmation of predictions
made in [9], [12] and [6]. Our method relies on studying the number of pivotal
vertices and open paths, combined with a delicate coupling argument.
