From Latin 'demittere' (to send down) — originally a legal term for property transfer; death became 'demise' because it triggers the transfer.
A person's death; the end or failure of an enterprise or institution; (law) to convey or grant an estate by will or lease.
From Anglo-French demise, the feminine past participle of Old French demettre (to dismiss, to put aside, to lay down office), from Latin dēmittere (to send down, to lower, to let fall), composed of dē- (down, away from) + mittere (to send, to let go, to release). Latin mittere is central to the Latin lexicon: it produces mission, missile, emit, commit, permit, submit, remit, and transmit — all built on the idea of sending. The original English legal sense was the transfer of an estate or sovereignty
The phrase 'the demise of the Crown' does not mean the death of the monarch — it means the instantaneous transfer of sovereignty from the dying monarch to the successor. In English constitutional law, the Crown never dies: upon the death of the sovereign, the Crown is 'demised' (sent down) to the heir. This legal fiction is the origin of the phrase 'The King is dead