I think women have to come to terms with the fact that men now and then need a break or that they just wish to finish their conversation. When turning down a request for one of the reasons already described, the man can politely make up for his 'false refusal' by promising a later dance to the women who asked him. Some men even leave the room when a new dance begins because they then will not be considered as dancing partners - and a 'false refusal' therefore is not necessary. But I think they should better admit their need for a break openly instead of taking flight. My experience taught me that women also use 'false refusals' out of their need for a break - when their legs or shoes hurt or they simply feel like having a bit of fresh air.
Men understand and accept such behaviour.
On Special Dances the relation of male versus female dancers is far more balanced. When I was in Erlangen a few weeks ago, there even were considerably more male than female dancers. When dancing Plus, a higher number of men than women is almost the normal standard. Of course it is not quite fair to ask people to wait for different and future events. Instead, we ourselves should try to do something about the present situation.