Answers to employment law issues are almost always very fact specific. An employment lawyer would need more information to give you a careful evaluation. However, I can share that employers generally have broad discretion to manage their workforce. Employers can even make decisions or enforce expectations that are unfair, unreasonable, or stupid -- and its usually not illegal. There are exceptions, however. For example, employers may not take adverse action against an employee (like a PIP) because of an employee's age, race, color, national origin, religion, gender, or disability. Otherwise, an employer is free to enforce its performance expectations, even if you disagree with those expectations. Good luck.
Yes, if you are an employee "at will", ( no union or individual employment contract ) an employer can fire you for a good or bad reason, an unjust reason, or no reason at all. You can not be fired based on an illegal reason ( race, national origin, sex, religion, disability, age, etc, because laws prohibit employers from taking employment actions based on those reasons. In sum, if the laws say that you can not be fired for reasons A, B, and C, and they fire you based on reason "D" , then the firing wont be illegal unless you can show that the real reason was for A, B or C, and that the reason they gave , "D" , is just a pretext to cover illegal discrimination. You need to talk to an employment lawyer in your state to look at your specific situation . A good source to find on one is the National Employment Lawyers Association ( google NELA), they have a feature on their web site to find employment lawyers that represent workers in your state.
Legal disclaimer: This response is meant to be information only and should not be considered to be legal advice. This information is not meant and should not be construed to be the formation of an attorney client relationship. Employment laws may vary by state and you should contact an attorney in your state to see if a state law may be applicable to your situation.