We scrambled to investigate and fix this particular instance (and previous unrelated instances where they'd had problems). When we realised that they were simultaneously screaming about how shit we were, we put it back on the shelf.
Fixing fundamental basic functionality of your app should not be classified as having "burnt a bunch of time investigating this".
Right, but this is where your response baffles me: they've reported a genuine issue with the implementation, so why not fix it for everybody instead of "put[ting] it back on the shelf" and letting others suffer too?
It sort of sounds like "they complained about us, so fuck them and their issue" (except it's not just their issue). Wouldn't it be better to work around disagreements to benefit everybody, instead?