We consider branching Brownian motion on the real line with absorption at
zero, in which particles move according to independent Brownian motions with
the critical drift of −2​. Kesten (1978) showed that almost surely this
process eventually dies out. Here we obtain upper and lower bounds on the
probability that the process survives until some large time t. These bounds
improve upon results of Kesten (1978), and partially confirm nonrigorous
predictions of Derrida and Simon (2007)