  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 $-\sqrt{2}$. 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).
