During his youth, Alkan was esteemed as one of the greatest ever pianists. However, two events caused Alkan to withdraw Parisian society - the birth of his illiegitimate son, Delaborde, and the appointment of the inferior Marmontel as head of piano at the conservatory. Ronald Smith also cites Chopin's death as one of the major factors that influenced Alkan's complete withdrawal.
Asside from letters to and from Ferdinand Hiller, his contact with the outside world was virtually nil. Alkan taught piano, but didn't perform in public again until his final years (by that time, his technique had begun to decay).
Alkan performed very rarely in public, and his masterpieces collected dust for decades.
Composers such as Rubinstein, Ravel, and Rachmaninov admired Alkan's music, but did little to champion it.
Busoni's contraversial performance of Alkan didn't really help the latter's cause much, as Busoni performed the Frenchman's Cadenza to Beethoven's Third Concerto in Berlin in those nationalistic pre-WW1 years.
Besides Busoni, Smith, Ogdon, Petri, and Lewenthal also championed Alkan's music. However, it was not until Hamelin's recordings of Alkan in the 90s that truly definitive recordings begun to emerge.
To sum up:
At no point since the 1840's has Alkan been famous among any but the most erudite pianists or music enthusiasts.