Como dizer “Idade avançada” em inglês

Acho que uma opção melhor seria "advanced age" ou "old age".

Concordo com o Simon em relação a "advanced age", por falar nisso, "advanced age" é a opção que o jornal britânico 'Dailymail' utilizou. Confiram o trecho.

''Pontiff, 85, says strength 'no longer adequate due to his advanced age'; 'I have had to recognise my incapacity to adequately fulfill the ministry'.''

"Declining" aplica-se melhor a "health". Veja o exemplo abaixo:

Pope Benedict XVI surprised the world and left the Catholic church stunned when he announced he was to resign, citing his age and declining health. The Guardian

I don't recall hearing "declining age" used with humans. It's a confusing term. It sounds like "as people get younger".

"Old age" is blunt, perhaps unkind. I would suggest Donay's "advanced age", but you will also hear "golden years", "senior years", etc.