'non-storing' is a Modern English compound formed from the prefix 'non-' (from Latin 'non', meaning 'not') combined with 'storing', the present participle of the verb 'store'.

'store' (verb) entered Middle English via Old French (e.g. 'estorer') meaning 'to supply or put aside'; the present participle 'storing' was combined with the productive English prefix 'non-' in Modern English to form 'non-storing' (literally 'not storing').

Originally a literal negative of the action 'storing' (i.e., 'not storing'), it has been used in technical contexts to describe systems or modes that do not retain data; the core sense (not keeping/retaining) has remained consistent while applications narrowed in computing and technical usage.