Jointly optimizing power allocation and device association is crucial in Internet-of-Things (IoT) networks to ensure devices achieve their data throughput requirements. Device association, which assigns IoT devices to specific access points (APs), critically impacts resource allocation. Many existing works often assume all data throughput requirements are satisfied, which is impractical given resource limitations and diverse demands. When requirements cannot be met, the system becomes infeasible, causing congestion and degraded performance. To address this problem, we propose a novel framework to enhance IoT system robustness by solving two problems, comprising maximizing the number of satisfied IoT devices and jointly maximizing both the number of satisfied devices and total network throughput. These objectives often conflict under infeasible circumstances, necessitating a careful balance. We thus propose a modified branch-and-bound (BB)-based method to solve the first problem. An iterative algorithm is proposed for the second problem that gradually increases the number of satisfied IoT devices and improves the total network throughput. We employ a logarithmic approximation for a lower bound on data throughput and design a fixed-point algorithm for power allocation, followed by a coalition game-based method for device association. Numerical results demonstrate the efficiency of the proposed algorithm, serving fewer devices than the BB-based method but with faster running time and higher total throughput.