Every year, thousands of people suffer from skull damage and require personalized implants to fill the cranial cavity. Unfortunately, the waiting time for reconstruction surgery can extend to several weeks or even months, especially in less developed countries. One factor contributing to the extended waiting period is the intricate process of personalized implant modeling. Currently, the preparation of these implants by experienced biomechanical experts is both costly and time-consuming. Recent advances in artificial intelligence, especially in deep learning, offer promising potential for automating the process. However, deep learning-based cranial reconstruction faces several challenges: (i) the limited size of training datasets, (ii) the high resolution of the volumetric data, and (iii) significant data heterogeneity. In this work, we propose a novel approach to address these challenges by enhancing the reconstruction through learnable symmetry enforcement. We demonstrate that it is possible to train a neural network dedicated to calculating skull symmetry, which can be utilized either as an additional objective function during training or as a post-reconstruction objective during the refinement step. We quantitatively evaluate the proposed method using open SkullBreak and SkullFix datasets, and qualitatively using real clinical cases. The results indicate that the symmetry-preserving reconstruction network achieves considerably better outcomes compared to the baseline (0.94/0.94/1.31 vs 0.84/0.76/2.43 in terms of DSC, bDSC, and HD95). Moreover, the results are comparable to the best-performing methods while requiring significantly fewer computational resources (< 500 vs > 100,000 GPU hours). The proposed method is a considerable contribution to the field of applied artificial intelligence in medicine and is a step toward automatic cranial defect reconstruction in clinical practice.