  We consider the Airy$_1$ process, which is the limit process in KPZ growth
models with flat and non-random initial conditions. We study the persistence
probability, namely the probability that the process stays below a given
threshold $c$ for a time span of length $L$. This is expected to decay as
$e^{-\kappa(c) L}$. We determine an analytic expression for $\kappa(c)$ for all
$c\geq 3/2$ starting with the continuum statistics formula for the persistence
probability. As the formula is analytic only for $c>0$, we determine an
analytic continuation of $\kappa(c)$ and numerically verify the validity for
$c<0$ as well.
