Why did this show fail?

No clue. All is fine except for the final episode.

Galactica found a clever new angle for the show with relevance to the reality while coming from a show which was a cheap attempt to cash in on the star wars craze.

V did the exact opposite and became a reactionist, fearmongering show without a shred of imagination. The scifi elements coped out to be some metaphysical crap - blue energy floating through the room, some esoteric bliss... all that kind of *beep* people who like science fiction usually hate, because it is not science at all, it contradicts it.
And when it comes to technology it was clear that the alien forces could have erradicated the resistence easily with all those devices shown in the first episodes. So their attept to fight a war - especially a "clean one" - was rediculous to a mind-numbing degree.
The original show was grittier and it already worked. For its time it was in every way better than the new V ever became for our time.

Because it didn't have the heart the original did.

The show started off alright but then lost its way halfway through the first season. Taking the show off the air after only four episodes also made it lose momentum. It all points to the fact that it was rushed into production without really mapping out the show's story. I have a feeling not even the producers knew what the visitors' motives for coming to Earth were at first and just said to themselves "we'll deal with that later". The second season was actually quite fun, but you could tell they were just making it up as they went.

I thought it was a mistake to put it on ABC to be honest. Networks like ABC, CBS, and NBC will kill a show quickly if it doesn't do the numbers. It takes time to build a science fiction show. SyFy seemed to know this and gave BG the proper support both financially and time-wise to build a good series. These two things are essential as well as good writing, directing, and acting.

It was a brilliant show, it only got axed because ABC is notorious for that!