Due to process variation in nanoscale manufacturing, there may be permanently missing connections in information processing hardware. Due to timing errors in circuits, there may be missed messages in intra-chip communications, equivalent to transiently missing connections. In this work, we investigate the performance of message-passing LDPC decoders in the presence of missing connections. We prove concentration and convergence theorems that validate the use of density evolution performance analysis. Arbitrarily small error probability is not possible under miswiring, but we find suitably defined decoding thresholds for communication systems with binary erasure channels and peeling decoders, as well as binary symmetric channels and Gallager A decoders. We see that decoding is robust to missing connections, as decoding thresholds degrade smoothly.