Можно решить данную проблему, изменив после запуска процесса, его лимиты.

#!/bin/sh

### BEGIN INIT INFO
# Provides: pgbouncer
# Required-Start: $local_fs $remote_fs $network $syslog $named
# Required-Stop: $local_fs $remote_fs $network $syslog $named
# Should-Start: postgresql
# Default-Start: 2 3 4 5
# Default-Stop: 0 1 6
# Short-Description: start pgbouncer
# Description: pgbouncer is a connection pool server and replication
# proxy for PostgreSQL.
### END INIT INFO

PATH=/sbin:/bin:/usr/sbin:/usr/bin
NAME=pgbouncer
DAEMON=/usr/sbin/$NAME
PIDDIR=/var/run/postgresql
PIDFILE=$PIDDIR/$NAME.pid
OPTS="-d /etc/pgbouncer/$NAME.ini"
RUNASUSER="postgres"
LIMIT="prlimit --pid $PID --nofile=65535:65535"

# Include pgbouncer defaults if available
if [ -f /etc/default/pgbouncer ] ; then
. /etc/default/pgbouncer
fi

# Exit if we were uninstalled with the config still there
test -x $DAEMON || exit 0

# Check if configuration exists
test -f $CONF || exit 0

. /lib/lsb/init-functions

SSD="start-stop-daemon --pidfile $PIDFILE --exec $DAEMON --quiet"

case "$1" in
start)
# Check if we are still disabled in /etc/default/pgbouncer
[ "${START:-}" = "0" ] && exit 0
log_daemon_msg "Starting PgBouncer" $NAME
test -d $PIDDIR || install -d -o postgres -g postgres -m 2775 $PIDDIR
$SSD --start --chuid $RUNASUSER --oknodo -- $OPTS 2> /dev/null
sleep 1
PID=$(pidof pgbouncer)
if [ $PID ]
then
prlimit --pid $PID --nofile=65535:65535
fi
log_end_msg $?
;;

stop)
log_daemon_msg "Stopping PgBouncer" $NAME
$SSD --stop --retry 30 --oknodo
log_end_msg $?
;;

reload | force-reload)
log_daemon_msg "Reloading PgBouncer configuration" $NAME
$SSD --stop --signal HUP --oknodo
log_end_msg $?
;;

restart)
# we would use "$SSD --status" here if it were available in squeeze
$SSD --stop --signal 0
if [ $? -eq 0 ] ; then
OLDPID=$(cat $PIDFILE)
log_daemon_msg "Invoking PgBouncer restart" $NAME
su -c "$DAEMON -R $OPTS 2> /dev/null" - $RUNASUSER
if [ $? -ne 0 ]; then
log_end_msg 1
log_warning_msg "could not contact running instance"
log_warning_msg "(If you changed the port number, run \"stop\" and \"start\" separately.)"
exit 1
fi
# sleep until the process has changed PID
for t in 0.1 0.2 0.2 0.5 1.0 1.0 2.0; do # 5s in total
NEWPID=$(cat $PIDFILE 2>/dev/null)
[ "$NEWPID" ] && [ "$NEWPID" != "$OLDPID" ] && break
sleep $t
done
$SSD --stop --signal 0
log_end_msg $?
else
$0 start
fi
;;

status)
status_of_proc -p $PIDFILE $DAEMON $NAME && exit 0 || exit $?
;;

*)
echo "Usage: /etc/init.d/$NAME {start|stop|reload|force-reload|restart|status}"
exit 1
;;
esac