In autonomous systems, planning and decision making rely on the estimation of the system state across time. In this work, we use a preference model to implement a fault management strategy that selects a unique estimated state at each time point. If this strategy is not carefully designed, it can lead to incomplete estimators that meet a dead-end in some scenarios. Our goal is to detect such scenarios at design time and to be able to blame a subset of preferences causing them; those can be proposed to the designer for revision. To do so, we propose a method for detecting dead-end scenarios, introduce preference relaxation, and apply a consistency-based meta-diagnosis approach for identifying the sets of "faulty" preferences for a given dead-end scenario. We build upon SAT solvers for checking estimator incompleteness, and for consistency checking during meta-diagnosis.