(Note that I'm writing this without having watched A Good Day...)
I think there's one fundamental flaw that some directors just don't know how to properly adapt in this franchise. And that is how the character acts and reacts to what's going on. What made the first movie so special is the situation in which the character was put into, it was a very unique type of story.
They tried to do almost the same thing with a different environment in Die Harder, but something didn't click. Then the same director does what it should've been done in the first place, in Die Hard With a Vengeance, raising the stakes, to open the game but without losing the one special element that worked with the original movie: the character and the situation. The movie got bigger, but it stayed true to the concept.
Live Free or Die Hard tried to raise the stakes once again, involving an even bigger scope. I think that movie is an entertaining action movie, but doesn't feel like Die Hard. Is just a bald Bruce Willis in a random (good) action movie.
I haven't seen A Good Day to Die Hard, but apparently the ongoing mistake of "getting bigger" (this time, leaving the country) is doing a lot of damage to the franchise.
I think they should re-think what made the best two movies work (personally, 1st and 3rd) and try to apply that logic to a new Die Hard movie. Back to basics. I think the James Bond franchise is a good example, in the sense that it got so off the rails with Die Another Day that they had to start from scratch with Casino Royale.
I know Die Hard is not that big of a franchise, but we have 5 movies already, and they plan to make a 6th one. Is still much longer than most franchises. So, I hope they realize what they're doing wrong to make a good, final, closing Die Hard movie.