The Liechtenstein name seems to be closely guarded. I can only find a very few examples of where a Prince has been 'demoted' to a lesser title and rank:
Prince Albrecht Johannes (born 1940), who in 1966 married morganatically. His wife became Baroness von Landskron, and in 1971 the Prince became Baron von Landskron.
Prince Franz Josef II bestowed these titles, and I've no idea why there was a six year delay for Albrecht Johannes (private family business?).
Prince Wilhelm (born 1922) renounced his rights and titles on his marriage in 1950, and was created Count von Hohenau by Franz Joseph II. But in 1980 Franz Josef reversed this decision and Wilhelm, his wife and children were re-established in name and title to the Princely rank. (A reward for good behaviour?)
Prince Ferdinand (1901-1981) married "not conforming to the laws of the Princely House" in 1925 and 1940 and his wives were created Countesses von Rietberg. His son, Johannes (Hanno) (1941-2003), born a Count von Rietberg, was granted the von und zu Liechtenstein name and Princely title in 1974 by Franz Josef II.
I can't see any Counts von (or und zu) Liechtenstein in any of the descendants of Prince Franz Josef I (1726-1781), from whom the current extended Princely Family descend.
sources: Burke's Royal Families of the World, Vol I, and Almanach de Gotha.