They are within their power to take it away - as long as they are not violating someone's Constitutional rights in doing so.
For example: Most employment in this country is "at will," which means the employment relationship can be ended by either party at any time. It's commonly said that an employer can fire an employee "for a good reason, a bad reason or no reason at all."
But the employer is limited by an employee's legal rights. The employee has a right under the first amendment to advocate forming a union. So even though the employer could have fired the employee for no reason at all, if they fire the person for advocating a union, the employee will have a cause of action for retaliatory discharge based on violation of his first amendment rights to freedom of speech and association.
Intent matters, and in court it's an issue of fact. The employer will come in with evidence of various legal reasons for firing the employee (lateness, poor performance, etc.) and the employee will counter with evidence that his performance was considered satisfactory until he exercised his first amendment right. The fact finder will decide what the true reason was for the firing.
Here, the governor has made the intent issue pretty easy.