EI refused, should i appeal?

I worked for a government company for 9 years, consistently ranking at the top of my team with a clean record and no disciplinary issues. Last year was tough due to family emergencies; I sought counseling and all available support, but I made a mistake at work. They suspended me and then terminated my employment. The union has filed a grievance on my behalf. Meanwhile, my EI claim was refused due to the termination. They advised me to appeal if I wish—can someone suggest the likelihood of success and the best path forward?