Background It has been suggested that impaired dissipation of slow-wave activity (SWA) in children with sleep-disordered breathing (SDB) may be a potential mechanism for daytime dysfunction. We aimed to examine whether resolution of SDB resulted in normalisation of SWA dissipation and whether this was associated with improved cognition and behaviour. Methods Children (aged 3–6 y) diagnosed with SDB and age-matched non-snoring control children were followed up for 3 y after a baseline study. At the follow-up, children were categorised into control (N = 13), resolved SDB (N = 15) and unresolved SDB (N = 14). Delta activity on the electroencephalogram over the sleep period was used to calculate SWA and a battery of cognitive assessments and behaviour questionnaires were conducted at both time points. Results There was no change in the average SWA between the baseline and follow-up and no differences between the groups. Cognitive and behavioural performance in the resolved group did not improve to control levels. However, decreased SWA at the beginning of the sleep period (β = −0.04, p = 0.002) and a decrease in obstructive apnoea–hypopnoea index (β = −2.2, p = 0.022) between the baseline and follow-up predicted improvements in measures of sustained attention. Increased SWA at the beginning of the sleep period between the baseline and follow-up predicted worsening of externalising behaviour (β = 0.02, p = 0.039). Conclusions This study suggests that resolution of SDB is not associated with changes in the dissipation of SWA. However, the association between decreases in SWA and improvements in cognitive and behavioural outcomes suggest that irrespective of disease, children whose quantitative sleepiness improves have improved attention and reduced externalising behaviours.