'non-continuous' is formed by the prefix 'non-' (from Latin 'non', meaning 'not') attached to 'continuous', which originates from Latin 'continuus' (from 'continuare').

'continuous' passed into English via Old French/Medieval Latin from Latin 'continuus' (from the verb 'continuare' meaning 'to join together or make continuous'); the modern compound 'non-continuous' is a straightforward negative formation using the productive English prefix 'non-'.

Originally rooted in Latin senses of things 'being joined together' or 'uninterrupted', the element 'continuous' kept that core meaning; 'non-continuous' therefore simply developed as the transparent negation meaning 'not uninterrupted' or 'interrupted/occasional'.