Yes, it's both possible and legal for your health insurance company to drop you under certain circumstances. Being aware of when and why this can happen is important for your financial well being and peace of mind.
The good news is that health insurance companies in the US are regulated by various laws on both state and federal levels. This means that technically they can only drop members who meet (or don't meet) specific criteria.
The bad news, of course, is that sometimes those laws are confusing and their application to real-life situations involves a lot of fine print which not all customers understand. Furthermore, while you can not be dropped for just any reason, you can be dropped at any time the company deems proper.
Specific details of your plan will be outlined in the paperwork provided by your employer and/or your insurance company, so familiarizing yourself with that information is your most important safeguard against being unexpectedly dropped from your plan.
With that said, the reasons for which an insurance company can drop a member fall into a few general categories, and being aware of those is a good first step. In general, then, your health insurance company...