'occasionally-allowed' originates from Modern English, specifically as a compound of 'occasionally' and 'allowed'. 'occasionally' ultimately originates from Latin, specifically the word 'occasionem' (via Old French 'occasion'), where the root 'occasio' is related to falling into or happening at an occasion; 'allow' (in 'allowed') originates from Old French, specifically the word 'alouer', where 'ad-' meant 'to' and Latin 'laudare' meant 'to praise/approve' (extended to 'permit').

'occasionally' changed from Latin 'occasio(nem)' to Old French 'occasion' to Middle English forms (occasion, occasional) and then to 'occasionally'. 'allow' changed from Old French 'alouer' to Middle English 'allowen' and eventually to modern English 'allow' (past 'allowed'), and the descriptive compound 'occasionally allowed' emerged by combining the adverb and past participle.

Initially, 'occasionally' meant 'on an occasion' and 'allow' meant 'to approve or praise' (later 'to permit'); over time these became the modern senses and were combined into the adjectival phrase meaning 'permitted on some occasions'.