Well yes you're right, the log files contains only one day logs. But with this condition i wont be check the job when not ran, so i modified little and used like this , please let me know if done some thing wrong.

# Loop to check the Job1 <Send To CM started properly or not>
if [ $min -ge 1 -o $min -lt 30 ]; then
count=`grep -ic ": $hr:01.*SendToCM: Start:" $logpath`
elif [ $min -ge 30 -o $min -le 59 ]; then
count=`grep -ic ": $hr:30.*SendToCM: Start:" $logpath`
fi
if [ $count -eq 0 ]; then
echo -e "\nThe Job1 Send To CM is not started as schdueld at 1 and 30" >> mail.log
fi

i will mail the mail.log at last after checking for other jobs too