Scenario 1: An empty chest has a comparator measuring it. The comparator is off. A dropper is placed above the chest, pointing into it. An item is put into the dropper, and it is powered. The item goes into the chest, but the comparator does not update, and remains off.

Scenario 2: A chest with an item in it has a comparator measuring it. The comparator is on. A dropper is placed above the chest, pointing into it. An item is put into the dropper, and it is powered. The item goes into the chest (now contains two items), and the comparator turns off.

Note: I believe it is to do with the chest having a block above it, keeping it closed. The comparator updates as usual if the dropper is to the side rather than above, but the same issue arises again if I place any other solid block above the chest.