Welcome to China...Breaching a contract here or not respecting the terms of an agreement is as common as drinking tea.

It is also possible that because of the new Social Security legislation, your employer considers that he doesn't need to cover your health insurance expenses anymore even though they were stipulated in your employment contract. Indeed, with the new law, you're covered by the national health insurance, therefore, your employer can be reluctant to pay your health insurance together with the national one and decided to stop paying your normal health insurance.

Now, you can ask explanations to your school on the reasons why they cancelled your health insurance, and you can also try to remind them that the payment of your "health insurance" bills were agreed on the contract (providing you have a copy of it, some company asks you to sign the contract, but never returns it to you). If you're not satisfied with their answer or their methods, you can either sue the school (but a Chinese court will always stand on the side of Chinese interests or parties) or quit the school (but you'll get a really hard time to get a new visa).....

Maybe somebody can hopefully give you a 3rd solution.

Next time, if you get again this kind of insurance allowances, ask the company/school to pay half/full year of the insurance.

first and formost obtain documentation of what happened (email a request to your fao and dont be obvious simply ask for an explaination)
start contacting other schools to apply for a job.
try to negociate out of the contract (you need a reference letter from them) 
some people say the local PSB will help you, try it and see.
contact SAFEA (check online for the local number) 

if all fails sweat it out until your contract ends. this is china lieing cheating and manipulating are signs of intelligence here. people casn hate me call me a racist even though i say it has to do with growing up here and living here. but that is the truth and ripping off a foreigner gets bonus points. the entire country will close ranks against you. this is china.

goodluck