Real-world sensing systems are inherently imperfect: sensors may fail, intermittently disconnect, operate with asynchronous sampling rates, and be subject to noise, leading to measurement streams that are irregular, incomplete, and heterogeneous. Nevertheless, sensing strategies for real-time state reconstruction typically assume synchronous and continuously active sensors, a constraint that substantially limits their applicability in operational environments. In this work, we introduce fault-tolerant sparse sensing strategies in the context of shallow recurrent decoders (SHRED) to enable high-dimensional state estimation from sparse, asynchronous, and missing sensor measurements. Specifically, we consider naive imputation strategies, fault-tolerant recurrent temporal encoders, and we introduce four different transformer-based masking mechanisms to make SHRED explicitly aware of sensor availability through the binary data-availability mask. Moreover, we further introduce a multi-step decoding training objective for SHRED, resulting in smoother latent trajectories and more robust predictions. Throughout a synthetic benchmark and three real-world problems in hydrodynamic and ocean modeling, we show that (i) transformer-based masking mechanisms outperform standard imputation techniques and fault-tolerant recurrent architectures, (ii) the multi-step decoding training objective enhances reconstruction fidelity and robustness in the presence of heterogeneous missing-data patterns, while (iii) the computational efficiency of SHRED is preserved, with no additional inference-time overhead.

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