The nuclei segmentation of hematoxylin and eosin (H&E) stained histopathology images is an important prerequisite in designing a computer-aided diagnostics (CAD) system for cancer diagnosis and prognosis. Automated nuclei segmentation methods enable the qualitative and quantitative analysis of tens of thousands of nuclei within H&E stained histopathology images. However, a major challenge during nuclei segmentation is the segmentation of variable sized, touching nuclei. To address this challenge, we present NucleiSegNet - a robust deep learning network architecture for the nuclei segmentation of H&E stained liver cancer histopathology images. Our proposed architecture includes three blocks: a robust residual block, a bottleneck block, and an attention decoder block. The robust residual block is a newly proposed block for the efficient extraction of high-level semantic maps. The attention decoder block uses a new attention mechanism for efficient object localization, and it improves the proposed architecture's performance by reducing false positives. When applied to nuclei segmentation tasks, the proposed deep-learning architecture yielded superior results compared to state-of-the-art nuclei segmentation methods. We applied our proposed deep learning architecture for nuclei segmentation to a set of H&E stained histopathology images from two datasets, and our comprehensive results show that our proposed architecture outperforms state-of-the-art methods. As part of this work, we also introduced a new liver dataset (KMC liver dataset) of H&E stained liver cancer histopathology image tiles, containing 80 images with annotated nuclei procured from Kasturba Medical College (KMC), Mangalore, Manipal Academy of Higher Education (MAHE), Manipal, Karnataka, India. The proposed model's source code is available at https://github.com/shyamfec/NucleiSegNet.