This paper presents a Failure-Aware Access Point Selection (FAAS) method aimed at improving hardware resilience in cell-free massive MIMO (CF-mMIMO) networks. FAAS selects APs for each user by jointly considering channel strength and the failure probability of each AP. A tunable parameter \(α\in [0,1]\) scales these failure probabilities to model different levels of network stress. We evaluate resilience using two key metrics: the minimum-user spectral efficiency, which captures worst-case user performance, and the outage probability, defined as the fraction of users left without any active APs. Simulation results show that FAAS maintains significantly better performance under failure conditions compared to failure-agnostic clustering. At high failure levels, FAAS reduces outage by over 85\% and improves worst-case user rates. These results confirm that FAAS is a practical and efficient solution for building more reliable CF-mMIMO networks.