Large Language Models (LLMs) have significantly advanced sentiment analysis, yet their inherent uncertainty and variability pose critical challenges to achieving reliable and consistent outcomes. This paper systematically explores the Model Variability Problem (MVP) in LLM-based sentiment analysis, characterized by inconsistent sentiment classification, polarization, and uncertainty arising from stochastic inference mechanisms, prompt sensitivity, and biases in training data. We analyze the core causes of MVP, presenting illustrative examples and a case study to highlight its impact. In addition, we investigate key challenges and mitigation strategies, paying particular attention to the role of temperature as a driver of output randomness and emphasizing the crucial role of explainability in improving transparency and user trust. By providing a structured perspective on stability, reproducibility, and trustworthiness, this study helps develop more reliable, explainable, and robust sentiment analysis models, facilitating their deployment in high-stakes domains such as finance, healthcare, and policymaking, among others.