The iterative algorithms employed to decode Low-Density Parity-Check (LDPC) codes are not guaranteed to converge to a valid code word for every receive word. The goal of Early Termination (ET) is to prevent the waste of resources in such cases. In this paper, we conduct an analysis of the suitability of ET criteria by tracking the evolution of parameters available from decoder-internal states. We find that the commonly selected parameters, e.g., the mean Log-Likelihood Ratio (LLR) magnitude or the fraction of satisfied parity checks, result in similar probabilities of detecting non-converging receive words. We propose a novel criterion for Early Give-Up (EGU) and evaluate its performance using a cost metric based on the retransmission of individual code blocks initiated by higher-layer protocols.