State-of-the-art KBQA models assume answerability of questions. Recent research has shown that while these can be adapted to detect unaswerability with suitable training and thresholding, this comes at the expense of accuracy for answerable questions, and no single model is able to handle all categories of unanswerability. We propose a new model for KBQA named RetinaQA that is robust against unaswerability. It complements KB-traversal based logical form retrieval with sketch-filling based logical form construction. This helps with questions that have valid logical forms but no data paths in the KB leading to an answer. Additionally, it uses discrimination instead of generation to better identify questions that do not have valid logical forms. We demonstrate that RetinaQA significantly outperforms adaptations of state-of-the-art KBQA models across answerable and unanswerable questions, while showing robustness across unanswerability categories. Remarkably, it also establishes a new state-of-the art for answerable KBQA by surpassing existing models