LLM training is scaled up to 10Ks of GPUs by a mix of data-(DP) and model-parallel (MP) execution. Critical to achieving efficiency is tensor-parallel (TP; a form of MP) execution within tightly-coupled subsets of GPUs, referred to as a scale-up domain, and the larger the scale-up domain the better the performance. New datacenter architectures are emerging with more GPUs able to be tightly-coupled in a scale-up domain, such as moving from 8 GPUs to 72 GPUs connected via NVLink. Unfortunately, larger scale-up domains increase the blast-radius of failures, with a failure of single GPU potentially impacting TP execution on the full scale-up domain, which can degrade overall LLM training throughput dramatically. With as few as 0.1% of GPUs being in a failed state, a high TP-degree job can experience nearly 10% reduction in LLM training throughput. We propose nonuniform-tensor-parallelism (NTP) to mitigate this amplified impact of GPU failures. In NTP, a DP replica that experiences GPU failures operates at a reduced TP degree, contributing throughput equal to the percentage of still-functional GPUs. We also propose a rack-design with improved electrical and thermal capabilities in order to sustain power-boosting of scale-up domains that have experienced failures; combined with NTP, this can allow the DP replica with the reduced TP degree (i.e., with failed GPUs) to keep up with the others, thereby achieving near-zero throughput loss for large-scale LLM training.