Snapedom

While HBP was much better plotted than DH it did give us one magical element that shouldn't have been introduced, which is Felix Felicis. It is almost as bad as Time Turners as a plot hole waiting to happen. I don't think Rowling is aware that this is what those two are (and in a different way the whole reversal of wandlore in DH), but really, when you have this super-potion that gives you extra edge, both sides have at their disposal an expert potion maker (the same one), who himself is constantly walking on a razor-blade, don't tell me this super-potion hasn't been put to use by one or both sides many times over. So what if it takes 6 months to brew if you have the facility to do so on an ongoing basis? Severus would have been stupid not to start a batch the moment his Dark Mark started returning, and for all we know he may have had some lying around just in case, the same as Slughorn. I mean, the man was in hiding for a year and shows up with an entire cauldron of the stuff - was he brewing while moving houses all the time or was this Severus' stock?

OK, so you can't take it constantly because of long-term effects, but any Slytherin worth his salt (and any uber-utilitarian Gryffindor) will have some around to take when s/he has warning that a critical event is afoot. For instance, the night of the battle of the Department of Mysteries - how did Severus manage to time his warning to the Order so that Harry was still safe but Severus could still get away with Voldemort by saying he expected everything to be over by the time he issued his warning? And as a bonus, one of Severus' personal enemies got killed! Obviously he took some Felix when Umbridge dismissed him. But if Dumbledore had Felix available, why didn't the Horcrux hunt go any better? I don't think there was anything he could have done about the cup even with the best help of Felix, and Mundungus may have stolen the locket very soon after Sirius' death, so perhaps Felix couldn't have helped much there either, but why didn't Dumbledore find the diadem? Felix should have directed him to it. And if Severus had Felix, and he had warning that Voldemort was on the way to Hogwarts, why didn't he manage to avoid being killed and nearly missing the opportunity to transmit essential information to Harry? Or did he?

On top of that you can ask yourself if Dumbledore ever had the house-elves dose Harry with Felix when he expected Harry to need some extra luck such as the night Harry went after the Philosophers' Stone or the night of Buckbeak's hearing-execution (which was also on a full moon).