'reinvigorate' originates from the Latin prefix 're-' plus the verb 'invigorate', which ultimately comes from Late Latin 'invigorare', where 're-' meant 'again' and Latin 'vigor' meant 'liveliness' or 'strength'.

'invigorate' came into English from Late Latin 'invigorare' (via French influence) in the early modern period, and 'reinvigorate' was formed later by adding the prefix 're-' to mean 'to give vigor again' or 'to restore vigor', resulting in the modern English 'reinvigorate'.

Initially, the root sense was 'to give vigor' or 'to make lively'; over time the compounded form came to be used specifically for 'restoring or increasing energy, strength, or enthusiasm' (i.e., giving vigor again).