It looks, there's new regulation/demand by Foreign Expert Bureau (SAFEA) that Non can get Working permit, only if his/hers BA was completed in English speaking country, one Chinese placement agent told me.

Jobs advertisers won't contact you/reply, if they can't place you to the school, or if they are sure SAFEA won't grant WP to Non, what is norm in all big cities and everywhere by the coast of China.

Don't expect replies from adverts 'We filled the position. We'll keep your CV on file and if opportunity arise, we'll contact you again...', what is usual reply at Western English school. It is just polite manner, but Chinese advertisers don't do that.

Never mind 'no replies', and keep sending your CV continuously till you don't get an invitation for interview. I usually disregard 'Native English teacher' notice on the job advert, and send my CV anyway.

I was looking for the new position in March, and I get few offers as Non just in first 10-days. I would say, demand for Native English teachers in China is much bigger than actual availability of Natives, so you might have a chance.

Good luck!