<He has to protect her constantly from danger at every turn. Every time he saves her, she feels more indebted to him and the gratitude leads her to place him very high in her esteem to the point that she is also in love with him, just as he is with her.>
xhonzi, this is perfect. Putting Anakin and Padme out of harm's way as it happened in the movie denied the story this angle.
Padme, at least in my idea of who the character is, wouldn't allow herself to fall for Anakin based upon attraction alone. She would need another reason, a much more powerful reason, to "break the rules".
Matter of fact, Han grew on Leia because he was willing to do anything at all to keep her safe - rushing headlong into a stormtrooper squad, flying into an asteroid field, attacking a star destroyer, anything.