Accurate and reliable solar flare predictions are essential to mitigate potential impacts on critical infrastructure. However, the current performance of solar flare forecasting is insufficient. In this study, we address the task of predicting the class of the largest solar flare expected to occur within the next 72 hours. Existing methods often fail to adequately address the severe class imbalance across flare classes. To address this issue, we propose a solar flare prediction model based on multiple deep state space models. In addition, we introduce the frequency & local-boundary-aware reliability loss (FLARE loss) to improve predictive performance and reliability under class imbalance. Experiments were conducted on a multi-wavelength solar image dataset covering a full 11-year solar activity cycle. As a result, our method outperformed baseline approaches in terms of both the Gandin-Murphy-Gerrity score and the true skill statistic, which are standard metrics in terms of the performance and reliability.