Palpatine likely did know his former master Darth Plagueis' secrets to manipulating life itself, but it's entirely in his nature to allow Padame to die anyway, as he really, really enjoyed seeing everyone - especially his own servants - suffer.
And he didn't want Vader beholden to anyone besides himself, especially not someone who helped to organize the initial resistance to the Galactic Empire.
Basically, I just have to say, SPOILER ALERT: Palpatine was evil. :))