What are the reasons for the small numbers of female expatriates working for multinational corporations? 

The major reason for this is the fact that American society continues to hold to a large degree to traditional sex roles.

In our traditional society, men have been the breadwinners and women have been much less economically important.  Therefore, it has become normal for wives to go wherever their husbands’ jobs take them.  It has been much less normal for husbands to move around to accommodate their wives’ careers.  Because of this, women are less likely to leave the country for their jobs.  We still hold to the idea that men should not have to move around to follow their wives.