Evolution has us believe 'Survival of the fittest' dictates in the past what lived and died.
But it entirely overlooks the plain and simple fact that weaknesses probably played a bigger part in the survival of some races then strengths.
For one, having an insanely high birth rate is indicative of culture and physical weakness; it is a survival instinct pertaining to an understanding that the chance of living long enough to have children is low.
Additionally, when tribes conquered other tribes the weakest women would be the ones to be kept as slaves/wives for the masters sexual desires (who wants a strong one that makes horrible stuff like that hard) - not nice, but its true. Thus they would often foster children (illegitimate sure, but they still survived) in those societies, and generally because the families keeping those slaves were wealthy the kids had a higher chance of survival. Thus a races weakness was in many times the only thing which ensured their genes were passed on in some form.
So to drag all this back to your question; it is as others have already stated. Weaker Asian females with a desire to improve their potential of survival/children's potential for survival seek out white partners.
Now that Asia is becoming more of an economic force; if they also shift their culture to be more liberal and spread wealth/improve the bottom line we might find that less mixing occurs between Asian and Caucasian as the driver disappears.
We may also see a shift in the other direction.
There is always also the case of physique and what cultures determine as beautiful. Since Europe/Western culture (previously favoring the fat)/Africa (favoring a wide variety of intricacies) all began to adopt a similar view of attractiveness in Male (muscular/athletic) and female (slender/toned) Asian's stayed a 'little' bit different still favoring slender/toned females but having favored more feminine males. So when it came time for Asia to become more westernized over the last 20 years, the females wanted a westernized partner so many Asian males didn't fit the bill.
That said, in parallel to Asia becoming a more viable economic force, the world is also changing its world view on beauty. Females have remained relatively the same, but the shift is starting to see western culture move towards a preference for more feminine males. This also tends to imply we will see more white females taking Asian husbands. Debate exists as to why, personally I think its fairly obvious that people want less issues in their lives and more simplicity; for that reason the weakest of mind and body will thrive as they are the least likely to offend or cause problems.
All in all my whole post aims to point out how throughout history and even more nowadays, it is weakness that has and will drive evolution as much as it has been strength.
Realistically the only real examples of strength winning is the african domination of our other possible human ancestors throughout the world and the much more recent nordic migration resulting in western culture. Now that the world is moving towards equality, the ability for that style of hostile takeover has become impossible.