'nondismissible' originates from Modern English, specifically formed from the negative prefix 'non-' and the adjective 'dismissible', where 'non-' meant 'not' and 'dismissible' meant 'able to be dismissed'.

'dismissible' ultimately derives from Latin roots: from 'dimittere' (dis- + mittere 'to send'); 'dismiss' entered English via Old French/Latin, and the adjective 'dismissible' developed with the Latin-derived suffix '-ible' in Middle English. 'nondismissible' was later formed in modern English by adding the prefix 'non-'.

Initially, the root meant 'to send away' (Latin 'dimittere'); over time 'dismissible' came to mean 'able to be sent away, removed, or rejected', and 'nondismissible' evolved to mean 'not able to be dismissed' (often with legal/official force).