High-precision localization turns into a crucial added value and asset for next-generation wireless systems. Carrier phase positioning (CPP) enables sub-meter to centimeter-level accuracy and is gaining interest in 5G-Advanced standardization. While CPP typically complements time-of-arrival (ToA) measurements, recent literature has introduced a phase-only positioning approach in a distributed antenna/MIMO system context with minimal bandwidth requirements, using deep learning (DL) when operating under ideal hardware assumptions. In more practical scenarios, however, antenna failures can largely degrade the performance. In this paper, we address the challenging phase-only positioning task, and propose a new DL-based localization approach harnessing the so-called hyperbola intersection principle, clearly outperforming the previous methods. Additionally, we consider and propose a processing and learning mechanism that is robust to antenna element failures. Our results show that the proposed DL model achieves robust and accurate positioning despite antenna impairments, demonstrating the viability of data-driven, impairment-tolerant phase-only positioning mechanisms. Comprehensive set of numerical results demonstrates large improvements in localization accuracy against the prior art methods.