Demoted after car accident from full time to part time

With limited exceptions, an employer is free to fire an at-will employee who misses too much work since attendance is typically a basic requirement of the job. The exceptions to this are if an employee's absences are protected by: the FMLA (Family Medical Leave Act); the ADA (Americans with Disabilities Act); workers' compensation laws; state paid sick leave laws; or if they had available PTO. If any of these are applicable in your case, then your company can't terminate your employment. Otherwise, absent protection under a union/collective bargaining agreement or employment contract, your company is free to set the conditions of employment much as it sees fit (provided no form of actionable discrimination plays a role in your treatment). Finally, a doctor's note is not legally binding on an employer.

Yes, you can be demoted, have hours reduced, or even be terminated if you did not use (such as, for example, because you company was not covered or you were not eligible) FMLA leave for the absence or use paid time off (PTO) which you had earned for the absence. The law does not make employers retain employees or hold their jobs for  them when they are out for medical reasons unless they use leave, like FMLA leave, given them by law or use PTO; indeed, your employer could have terminated you immediately. The doctor's note does not control what you employer does; it is allowed to eliminate employees who do not or cannot work or who miss work, even for medical reasons, without using legally protected leave or PTO.