It seems that updating the init script and the Monit configuration to what's below solved my issue :
Code:
check process Sonarr with pidfile /home/pi/.config/NzbDrone/nzbdrone.pid
start program = "/usr/sbin/service nzbdrone start"
stop program = "/usr/sbin/service nzbdrone stop"
restart program = "/usr/sbin/service nzbdrone restart"
if failed host 127.0.0.1 port 8989 with timeout 60 seconds then restart
if changed pid then exec /etc/monit/pushbullet.sh
if 10 restarts within 10 cycles then exec "/etc/monit/pushbullet.sh"
if 11 restarts within 11 cycles then unmonitor
Thanks for your help guys!