Unless you had a contract, you were an at-will employee and therefore could be fired for any reason or no reason so long as it was not an unconstitutional reason such as based on race, gender, religion, etc. There is no harm in appealing.
I am a former federal and State prosecutor and have been doing criminal defense work for over 16 years. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012 and 2013. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. Martindale-Hubbell has given me its highest rating - AV Preeminent - in the areas of Criminal Law, Personal Injury, and Litigation. According to Martindale-Hubbell”AV Preeminent is a significant rating accomplishment - a testament to the fact that a lawyer's peers rank him or her at the highest level of professional excellence." Fewer than 8% of attorneys achieve an AV Preeminent rating. I also have the highest ranking – “superb” – on Avvo. Feel free to check out my web site and contact me. The above answer, and any follow up comments or emails is for informational purposes only and not meant as legal advice.
You should always appeal, you never know what might happen. That said, there is a good chance multiple latenesses will be considered a for cause termination. Employers need employees to be on time.
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