You are working in an at-will employment state. They can terminate you for any reason or no reason, provided it is not an illegal reason or a violation of public policy. Nothing you have listed here gives any indication of any illegal conduct by the employer. When you work for someone you need to get to work on time and perform the duties they have given you. If you can't do either of those basic requirements then you are not going to remain employed.
Best of luck.
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Like the other lawyer said...you are an at-will employee in Alabama. However, there are some places of employment where there are rules that limit the employer's right to fire you. Your place of employment might have a union, and there might be a collective bargaining agreement...although it doesn't appear that way from your question. Also, if the system of 'points' you described is enshrined in an employment agreement, you might have a claim.
Your termination may not make sense, but unless you had an employment contract, you can be terminated for any reason (excepting for a few exceptions: race, sex, religion, seeking workers' compensation benefits, having to serve on jury duty and national guard/reserve training), just as you are free to quit your job for any reason. Businesses have a right to run their company badly.