Quanvolutional Neural Networks (QNNs) have been successful in image classification, exploiting inherent quantum capabilities to improve performance of the traditional convolution. Unfortunately, the qubit’s reliability can be a significant issue for QNNs inference, since its logical state can be altered by both intrinsic noise and by the interaction with natural radiation. In this paper we aim at investigating the propagation of logical-shift errors (i.e. the unexpected modification of the qubit state) in QNNs. We propose a bottom-up evaluation reporting data from 13,322,547,200 logical-shift injections. We characterize the error propagation in the quantum circuit implementing a single convolution and then in various designs of the same QNN, varying the dataset and the network depth. We track the logical-shift error propagation through the qubits, channels, and subgrids identifying the faults that are more likely to cause misclassifications. We found that up to 10% of the injections in the quanvolutional layer cause misclassification and even logical-shifts of small magnitude can be sufficient to disturb the network functionality. Our detailed analysis shows that corruptions in the qubits’ state that alter their probability amplitude are more critical than the ones altering their phase, that some object classes are more likely than others to be corrupted, that the criticality of subgrids depends on the dataset, and that the control qubits, once corrupted, are more likely to modify the QNN output than the target qubits.