  If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete
subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is
an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup
$U$ in the horospheric group $N$, the Burger-Roblin measure associated to
$\Gamma$ on the quotient of the frame bundle is $U$-recurrent.
