I did read about how when it was first premiered it had little success, and I do know about his other works for violin but I was wondering if maybe (don't slap me too hard for this Beethoven lovers, because I am a HUGE Beethoven fan) he knew that the younger Paganini had him bested on the violin and his pride would not allow him to write more violin pieces, or was Beethoven's "arena" the piano and writing Symphonies? I think his Violin Concerto is fantastic and wish he would have written more concertos and other violin pieces. Did Beethoven ever hear a Paganini piece before he lost his hearing? I think I read somewhere that Paganini did not tour, or play much outside his native Italy until 1828, a year after Beethoven's death. Just curious.
Answer on Why did Beethoven write only one Violin Concerto?
Of all the violin concerto literature, there is some general agreement about the Beethoven fiddle concerto. As the author Irving Kolodin wrote in his biography of Beethoven, "The Interior Beethoven"
~ "He only wrote one violin concerto, but it is THE violin concerto."*
Maybe Luigi knew the same about his concerto, and left things be.
* I would have to add the Berg Violin Concerto as the other 'THE' violin concerto - there is growing consensus about this piece too.
best regards.