Though not 100%, the islands were probably named by Abraham Bristow who was an English whaler and sailor in 1806, in all likely hood he was probably looking for settlements and/or water and after exploring the main island of Auckland Island found this one and concluded that this area did not have much to offer and made a poor location for anything other than whaling. I could only find shaky sources on this but it looks like Mr. Bristow was looking for a place to build a small settlement for the whaling industry and these Islands were not conducive for human habitation at the time.

However this isn't the only use of the word in reference to islands that don't have much on them, at the time in the early 1800's there seems to be an informal fad for naming islands "disappointment"

I believe it was John C. Fremont in 1843 who was surveying an island in Utah, America and he named it so because he could find no game in which to hunt. It was later named to Fremont Island once a town was built near it.

There is also the Disappointment Islands located French Polynesia that were called "Islas Infortunadas" or "Unfortunate Islands" when Magellan could not find a proper water source. So while this island near New Zealand maybe the most acknowledged case I would argue that this boils down to sailor jargon that didn't have the same meaning as it does now. This may be a case more for etymologist than historians.