Going back through earlier saves, it looks like this first started happening some time during the Campbell mission - I have a save in Galvani's mansion where it was working fine, and then one near the start of the High Overseer's Office area (immediately after releasing Martin) where it isn't. Once it started happening it seems to have persisted; the heart isn't working in any saves beyond that point, up until after arriving back at the Hound Pits (at which point we realised that something was definitely amiss and stopped playing).
Are there any known ways to fix this or is it just going to be a case of reloading an old save and playing through again?