“How would the case’s failure equate to the death of the constitution?”
If Barry Obama is not a natural born citizen then he can constitutionsally never serve as POTUS. He can only be an imposter, and all of his pseudo-official actions would be null and void. If the courts conspire to ignore this inconvenient fact, then what other part of the U.S. Constitution are we or they bound to respect? If Barry’s inconvenient status can simply be ignored with a wink and a nod, then the Constitution is, in the memorable language of Chancellor Bethmann-Hollweg, “just a scrap of paper”.
That's a big "if", and the faiure of Berg's case doesn't make it true.
If Obama was born in Hawaii then he is a natural born citizen, regardless of any claims in Berg's suit.