'time-unlimited' originates from Modern English as a compound of 'time' and 'unlimited', where 'time' comes from Old English 'tima' meaning 'period or season' and 'unlimited' is formed from the prefix 'un-' + 'limited' (from Latin roots) meaning 'not having limits'.

'time' developed from Old English 'tima' (period/season) derived from Proto-Germanic '*tīmô'; 'limit' entered English via Old French and Latin 'līmes'/'līmit-' meaning 'boundary', becoming Middle English 'limit'; 'un-' was added in English to form 'unlimited', and the compound 'time-unlimited' is a later, transparent Modern English formation combining these elements.

Initially, 'time' denoted a period and 'unlimited' meant 'without limits' generally; over time the compound came to mean specifically 'not limited in time' or 'without a time limit'.