You say its young - does that mean recently acquired by you? And if so, where was it when you bought it - under shelter at a garden centre? Or inside somewhere? Because it could be transition shock - putting the plant straight outside in an exposed situation when its not experienced that before, and needed hardening off first.

Dear Nottinghamshire - if you are still alive, as of 2021, and if your Aucuba Japonica leaves are still drooping, may I inform you that, in my experience, Aucuba Japonica generally hates water, and, if it gets too much, it not only will droop, it, if the situation does not get drier, will kill itself graveyard dead on you, for sure.

What has helped me is to water it only a bit during summer droughts and, when I first plant it, to put a foot worth of medium size pine bark chips below it, and composed soil around it, so that it's root never stand in water, because it will always prefer death to that.

All the best, from rural North Carolina!