Japan’s Princess Mako will lose her status as royalty when she marries her fiance, Kei Komuro. Her aunt also lost her royal status when she married a non-royal twelve years ago. More here from the BBC. More recently, another princess gave up her status when she married another non-royal. Note that the Crown Prince married a non-royal, but kept both his royal status and his position in line for the throne.
The Japanese nation has been discussing whether women should have the right to succeed to the Chysanthemum Throne for some years. In 2005 a government panel issued a report that recommended that females be allowed to succeed but those recommendations have not yet been adopted. Some experts say royal women should keep their rights, even if that might lead to claimants to the throne through female descent.