This question was created with the hard-science tag, but I was asked to change it to science-based. I agreed with the change, and so it was made -
The actual problem here is that this isn't a bug.
The post notice comes up when a moderator sees that a question has the hard-science tag, and adds the post notice manually to the question and any answers that don't meet the requirements of the tag (it shows up in the revision history). As far as I can tell, I'm often the one who does this, just because I check the recent activity on the tag's page pretty regularly. For answers, I have a flowchart I use; for questions, the notice always gets added.
The thing is, nobody can tell when a question has the tag removed, because, save for a few short minutes while caching rears its ugly head, the question is no longer in the list of hard-science questions, and so I can't see it. This is when you need to flag the post for moderator attention, and one of us will hopefully remove the notice from the question and the answers as soon as possible.
The real bug, I feel, is that people don't flag posts they feel should or should not have the notice. We the moderators can't do anything if we don't know a question has just gotten the tag or has just lost it; we need people to tell us through a flag. It's explicitly stated in the tag wiki and tag wiki excerpt for the case of adding the tag, but maybe it should be made clearer that removal also requires moderator attention.
I suppose you could ask for this whole thing to be automated. It wouldn't take much work off of the mods, because most of our work around the tag involves judging whether or not an answer needs the post notice, and that probably can't be done by an algorithm (although maybe I should try automating my flowchart! Not really.). But it might save some time, in the long run.