With the steady increase in core counts per job in high performance computing facilities, systems and algorithms used for numerical simulations increasingly contend with disruptions caused by hardware failures and bit-level misrepresentations of computing data. In many numerical frameworks exploiting massive processing power, the solution of linear systems represents one of the most computationally intensive algorithmic components. With mean times between failures approaching minutes in HPC facilities, iterative solvers are particularly vulnerable to bit-flips.A new method named FT-GCR is proposed here that supplies the preconditioned Generalized Conjugate Residual Krylov solver with detection of, and recovery from, soft faults. The algorithm tests on the monotonic decrease of the residual norm and, upon failure, restarts the iteration within the local Krylov space. Numerical experiments on the solution of an elliptic problem arising from a stationary flow over an isolated hill on the sphere show the skill of FT-GCR in addressing bit-flips on a range of grid sizes and data loss scenarios. Best returns on fault tolerance and detection rates are obtained for larger corruption events. The computational and memory cost of the method is addressed, and savings in the presence of faults are quantified in terms of time to solution compared to unprotected runs. The simplicity of the method makes it easily extendable to other solvers with monotone convergence in a computable norm and a suitable candidate for algorithmic fault tolerance within integrated model resilience strategies.