息 combines 自 (nose) above 心 (heart), suggesting the breath that continues while the heart beats.
The top component 自 originally depicted a nose and later came to mean 'self' (people point to their nose when referring to themselves). The bottom component 心 is the heart. Together they evoke the quiet rhythm of breathing through the nose while the heart beats, which is what happens when you rest. This is a genuine traditional analysis, not a folk etymology.