Motivated by a study on visual implicit learning in young children with Autism Spectrum Disorder (ASD), we propose a robust functional clustering (RFC) algorithm to identify subgroups within electroencephalography (EEG) data. The proposed RFC is an iterative algorithm based on functional principal component analysis, where cluster membership is updated via predictions of the functional trajectories obtained through a non-parametric random effects model. We consider functional data resulting from event-related potential (ERP) waveforms representing EEG time-locked to stimuli over the course of an implicit learning experiment, after applying a previously proposed meta-preprocessing step. This meta-preprocessing is designed to increase the low signal-to-noise ratio in the raw data and to mitigate the longitudinal changes in the ERP waveforms which characterize the nature and speed of learning. The resulting functional ERP components (peak amplitudes and latencies) inherently exhibit covariance heterogeneity due to low data quality over some stimuli inducing the averaging of different numbers of waveforms in sliding windows of the meta-preprocessing step. The proposed RFC algorithm incorporates this known covariance heterogeneity into the clustering algorithm, improving cluster quality, as illustrated in the data application and extensive simulation studies. ASD is a heterogeneous syndrome and identifying subgroups within ASD children is of interest for understanding the diverse nature of this complex disorder. Applications to the implicit learning paradigm identify subgroups within ASD and typically developing children with diverse learning patterns over the course of the experiment, which may inform clinical stratification of ASD.