Check if your scripts name doesn't contain $SERVICE. If it does, it will be shown in ps results, causing script to always think that service is running. You can grep it against current filename like this:
#!/bin/sh
SERVICE=$1
if ps ax | grep -v grep | grep -v $0 | grep $SERVICE > /dev/null
then
echo "$SERVICE service running, everything is fine"
else
echo "$SERVICE is not running"
fi