It was in abeyance. Although there was support for Elizabeth to be made Princess of Wales as she approached her 18th birthday, even from among Welsh politicians, her father King George VI opted not to.

He felt that the title was solely the title of the wife of the heir apparent and to administer it to his daughter would ruin precedent as well as cause confusion when she married.

The male-preference primogeniture probably played a part in his decision as well when the king was younger, as there would have been the possibility of a younger brother appearing to supplant Elizabeth as heir apparent. As the Prince of Wales title is given only to the heir apparent, it couldn't have been given to a young Elizabeth, without the real possibility of it having to be taken from her and given to a younger brother.

Likely in the future, as the male-preference has been removed and it is now the oldest child of the sovereign who inherits the throne, we could in theory find a future Princess of Wales holding the title in her own right. A generation or two on the future at least, except in rather sad circumstances (unless Prince William's eldest son predeceases him before William becomes king, making the heir apparent on Williams ascending the front his then eldest surviving child - his daughter)

Pimlott, B., The Queen: Elizabeth II and the monarchy, London: HarperCollins, 2001