Aside from the World War 2 U.S. car production hiatus, Lincoln Continentals were produced through the 1948 model year. But 1949 brought totally restyled Lincolns and Edsel had died in 1943, so Ford leadership was not motivated to continue the line even though stylists had sketched some proposals based on the new Lincoln Cosmopolitan body.
Potential buyers were unhappy with the decision to drop the Continental line and hounded Ford to build new ones. By the early 1950s the company was prosperous again and there was money available to do just that. Edsel's youngest son, William Clay Ford, was made head of the project. As this Wikipedia entry indicates, the new car was called Continental Mark II and was cast as a separate brand, though marketed by Lincoln. It was conceived as a super-luxury car, priced at $10,000 -- around twice the average U.S. household income at the time. Only a coupé was produced, though Ford had a convertible built and some coupé owners later had their cars customized as cabriolets.
So far, I haven't been able to locate suitable examples from the styling competition for the Mark II on the internet. When I find such images, I'll post about them. For now, I'll compare styling of the original 1940 coupé with that of the Mark II.
The Continental Mark II was not a sales success, only around 3,000 being sold over its two years on the market. It high price was a limiting factor. I think its styling was another contributor. Despite its low stature, the car was massive -- not light and sporting looking like the original was. Moreover its styling was dull, boring. Making it look very mid-50s with fins and multiple paints might not have worked either. The best solution from today's perspective would have been a shorter (but not too short) car with more Retro hints. But that might not have sold well either, given buyer expectations in those stylistically flamboyant times.