Device/Model: Android NVIDIA Shield tablet
OS: Android 6.0.1
PFID: 3BDE52BE2CFC9C6B
Gameplay: Pass & Play off, Permadeath off
Now, reproducing this bug is super-complicated, so I will walk you through it very carefully.
Step 1. Use a healing ability. Any healing ability (minor staff of healing, Mokmurian's club, Cure, Major Cure, Mass Cure, Kyra's ability, whatever, it doesn't matter in the slightest), on any character, by any character, in any scenario, at any location.
If that healing ability actually worked, congratulations, that means you can't progress the daily challenge, now proceed to step 2. If it didn't work, you have successfully reproduced this bug.
Step 2. If healing is currently working for you, use another healing ability out of turn (I routinely used minor staffs drawn by a character resetting their hands at the start of the next character's turn, because why wouldn't I? And until the latest patch, that always worked fine.). At this point, healing will no longer work, but you will be able to progress on the daily challenge.
It really is that simple. I can't imagine why anyone is having the slightest difficulty reproducing this obvious, constant bug that makes the game unplayable.
Based on some of the ideas in this thread, I tried restarting my tablet. That was actually successful in putting me into the "healing works/challenges don't" mode of the game, and thus where Step 2 came from. Still, until and unless the game returns to having both healing and challenges working at the same time, I count the game as unplayable and won't be wasting my time with it anymore.