The details surrounding Padme's death are a little fuzzy, even to the biggest Star Wars fan.
The explanation we get from the movie, Revenge of the Sith, is that Padme had "lost the will to live" after almost being murdered by her husband, Anakin Skywalker. He force choked her after Obi-Wan revealed himself to have been hiding in her starship, believing that she brought him to end Anakin's streak of evil.
The idea of dying of "heartbreak" seems cheesy and is a cheap way of progressing the storyline. Padme still had her children to live for! I'm sure a former queen who participated in the beginning of the Clone Wars could understand the circumstances and not just give up.
This theory suggests that Darth Sidious hinted at having knowledge of the power to bring people back to life after studying under his master, Darth Plagueis, but he did not master it completely before killing him in accordance with the Rule of Two.
After Anakin sustained heavy wounds on Mustafar during the battle with his former master, Obi-Wan Kenobi, he was very close to death. Sidious saw that Anakin could potentially die due to his wounds so in order to save him, he transferred the life force of Skywalker's wife, Padme.
Although it may have seemed that Padme might have just "lost the will to live" because she suddenly became very weak during child birth, instead it was Sidious who used the Force and the power of midi-chlorians to take Padme's life and save Anakin's.
Although Sidious could have chosen anybody to use as a supply of life force for Anakin, killing Padme fueled a strong hatred in Anakin which would shape his path as a Dark Lord of the Sith.
So what do you guys think? Totally plausible, or complete bogus?