  It has been known for some time that solitons of the externally driven,
damped nonlinear Schr\"odinger equation can only exist if the driver's
strength, $h$, exceeds approximately $(2/ \pi) \gamma$, where $\gamma$ is the
dissipation coefficient. Although this perturbative result was expected to be
correct only to the leading order in $\gamma$, recent studies have demonstrated
that the formula $h_{thr}= (2 /\pi) \gamma$ gives a remarkably accurate
description of the soliton's existence threshold prompting suggestions that it
is, in fact, exact. In this note we evaluate the next order in the expansion of
$h_{thr}(\gamma)$ showing that the actual reason for this phenomenon is simply
that the next-order coefficient is anomalously small: $h_{thr}=(2/ \pi) \gamma
+ 0.002 \gamma^3$. Our approach is based on a singular perturbation expansion
of the soliton near the turning point; it allows to evaluate $h_{thr}(\gamma)$
to all orders in $\gamma$ and can be easily reformulated for other perturbed
soliton equations.
