Attosecond streaking is a powerful and versatile technique that allows the full-field characterisation of femtosecond to attosecond optical pulses. It has been instrumental in the verification of attosecond pulse generation and probing of ultrafast dynamics in matter. Recently, machine learning (ML) has been applied to retrieve the fields from streaking data (White and Chang 2019 Opt. Express27 4799; Zhu et al 2020 Sci. Rep.10 5782; Brunner et al 2022 Opt. Express30 15669–84). This offers a number of advantages compared with traditional iterative algorithms, including faster processing and better resilience to noise. Here, we implement a ML approach based on convolutional neural networks and limit the search to physically realistic pulses that can be specified with a small number of parameters. This leads to substantial reductions in both training and retrieval times, enabling near kHz retrieval rates. We examine how the retrieval performance is affected by noise, and for the first time in this context, study the effect of missing data. We show that satisfactory retrievals are still possible with signal to noise ratios as low as 10, and with up to $40\%$ of data missing.