'loss of appetite' is a compound phrase formed from the noun 'loss' (Modern English) and 'appetite' (Modern English, from Latin via French). 'Loss' is used here in the sense of 'the state of having lost or lacking' and 'appetite' in the sense of 'desire to eat.'

'loss' comes from Old English 'los' meaning 'destruction, deprivation' and developed into Middle and Modern English as 'loss.' 'Appetite' comes from Latin 'appetitus' (a longing, desire), from 'appetere' (to seek toward), passed into Old/Medieval French and Middle English as 'appetyt/appetite' and became the modern English 'appetite.' The phrase 'loss of appetite' arose in Modern English by combining these words to describe diminished desire to eat.

Individually, 'loss' originally referred broadly to 'destruction, deprivation' and 'appetite' to 'desire'; combined in English they came to mean specifically 'a diminished desire to eat.' Over time the phrase has retained this primary meaning and also acquired figurative uses (loss of appetite for X).