I noticed that it hadn't been busy making a silk button, but rather just stood still for 3 days.
This morning I found it hanging in the 'J' position, on the roof of the caterpillar castle. On closer inspection I saw there was no button whatsoever and that it's feet were just hooked into the fabric of the castle.
I recalled reading a post about this very thing, on the New Zealand Monarch Butterfly Trust website several years ago. Luckily I found the post and have copied it here, in the hope that it will also help others trying to save a fallen "J".
The above picture shows what I have done so far. Now I have to watch very carefully for when it is transforming into its chrysalis, just in case it falls.