Many older teachers get around this by obtaining an F visa, but F visas are expensive and inconvenient to get. In theory, it is also illegal to teach on a F visa, but many teachers do so anyway. Personally, I couldn't be bothered with all the hassle.

Actually, F's are not expensive if you're prepared to work for 'certain' recruiters in certain backwaters in China. Not inconvenient either! Even better, no medical to undergo!