We are interested in the recursive model (Y_n, n\ge 0) studied by Collet et al. (Commun Math Phys 1984)  and by Derrida and Retaux (J Stat Phys 2014). We prove that at criticality, the probability P(Y_n>0) behaves like n^{-2 + o(1)} as n goes to infinity; this gives a weaker confirmation of predictions made in Collet et al. (1984), Derrida and Retaux (2014) and Chen et al. (2019). Our method relies on studying the number of pivotal vertices and open paths, combined with a delicate coupling argument.

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