Over the years the bottle has collapsed from a vacuum forming inside, and I finally decided to vent this bottle. Once I opened it, and carefully squeezed the sides of the bottle to expand it back to its original round shape, I found that almost half the contents had vanished.
We had a few smaller bottles of this ink as well, and they also collapsed like this.
You might think that this is due to water somehow escaping from the bottle, but we use these bottles for several water-based products, and we have not seen this much shrinkage in those.
The only other conclusion is that the ink is undergoing some transformation which causes it to actually absorb the water chemically. This would probably be a hydrolysis reaction where a chemical bond breaks and a pair of hydrogen and hydroxyl ions attach themselves to the loose ends.
But then I weighed the bottle and it weighs about 320g, consistent with the weight of a 500ml bottle half-full of a mostly-water substance. So I suppose this is just water loss through the bottle and cap seal after all. If the water had been absorbed chemically, the weight should have been around 550g (500 g ink plus some allowance for the bottle).