What to do if my employer wants to stop paying for my health insurance?

You probably can't do anything if she wants to stop paying for health insurance. There are several problems:

1) First, if it's an oral agreement, proving its terms and existence if she states that she did not make it--it becomes your word against hers.

2) Even if she said she'd pay for your health insurance, if you were already working for her at the time, it might not be an enforceable agreement, but rather only an unenforceable promise; to be an agreement, there must have been consideration (or something given by you to bind the agreement), but if you were already working for her, it may be that there was no consideration given by you.

3) Unless you have a written employment contract protecting or guarantying your job, you are an employee at will, which means she could, for example, terminate you at will unless you agree to not receive the paid-for health benefits. This may be the biggest stumbling block, since even if you could prove there was an enforceable agreement to pay for your health insurance while you work for her, she could simply end your employment.

4) Related to the above, unless your salary is protected by a written agreement, even if you could hold her to an enforceable agreement to provide health insurance, she could cut your salary/wages or other benefits to compensate for the cost.

You were fortunate to have six years of paid-for health insurance, but it does not appear, unless you had an enforceable written employment agreement providing more job protection than you indicate, that you can compel your employer to keep providing it in the future.