What, do you think, was ultimately the downfall of Rhett and Scarlett's relationship? Pride....stubornness....vanity...?

For me it was blidness.
At Breakfast at Tiffany's Holly said something like her greatest fear is not recognizing sometjing belongs to her until it's gone (I'm sorry I don't remember exact qote).

That's Scarlet's problem. She imagined she loved Ashley. She belived in it so deeply, that she wasn't able to recognize that
1) Ashley she admires isn't the real one, he's never existed. The real man is lost, damaged & pathetic- nobody she'd ever admire, love or even like. Her love was a projection of her mind and she was too blind to see it.
2) She was so busy with her imaginated love to imaginated Ahley that she missed the fact that Rhett is the love of her life: the one who supports her, protects her, understands & acceprt exactly who she is.She was taking his love but she was to blind (& egocentric) to notice it.

Of course, Rhett's pride was a problem in this relationship. But I blame Scarlet more.She couldn't devide her dreams from reality. She was too blind to see what's going on in her life, what she needs & what she's given all the time... She was rejecting it year after year in the name of a childish fantasy until she lost it...

Scarlett always thinking she is in love with another man. Scarlett loves Scarlett and loves to flirt