Why is it so difficult to find a teaching job for Filipinos like me?
Don't you know Koreans think Filipinos are a lower class when it comes to teachers? They pay them less too. It's not fair, and it's discrimmination, but welcome to Korea, the land of discrimmination. Age and sex discrimmination are common.
Don't give up.
Get out there and start making friends. Go volunteer at one of the multi-cultural schools, women's shelters or orphanages. There are lots of ways to make connections that will lead to a job. If you want to know where to start, go to busan volunteer on facebook, they can lead you towards a place to volunteer.
We all get discouraged sometimes, but don't let it get you down, just let it be a lesson that you should dig in deeper and good things will come to you.
I'm considered 'old' as a teacher here in Korea, but I just kept knocking on doors until someone believed in experience over age and looks. Just keep believing the next one will be the one.