no idea!
Akiba Rubinstein

[COMMENT DELETED] Well, I thought he was nuts by that time, but I'm clearly wrong... It was probably something simple like he didn't have the money for travel, or didn't like to travel overseas. Is there any record of his having visited the states?

I don't know, but I have two ideas. First, in Kaikamjozov's book "The Genius and the Misery of Chess", he says that 1923 was when Rubinstein started to show the symptoms of his mental or emotional issues. So 1924, though he kept playing and having success, was around the begining of the troubled phase of his life. The other idea is that he was always very shy and reserved and all that, and I don't know that he had a lot of money. He might not have wanted to or might not had the money to get to NY which in those days was not as easy as it is today.

I've been searching for your answer on the interweb, but no success yet. But here is a link to "The five craziest and most brilliant grandmasters of all-time" which gave me a laugh during my search
http://amog.com/entertainment/celebrity/craziest-brilliant-chess-grandmasters-time/

Sadly, trysts, I wasn't able to find humor in the article. Rubinstein #4 on the list and Alekhine #3. Alekhine wrote the annotations to each of the 110 games of the international tournament at New York, 1924. I haven't read all of this tournament book yet (I've only just begun today), but maybe in there I will find a comment from Alekhine as to Rubinstein's absence from that event.

Sadly, trysts, I wasn't able to find humor in the article. Rubinstein #4 on the list and Alekhine #3. Alekhine wrote the annotations to each of the 110 games of the international tournament at New York, 1924. I haven't read all of this tournament book yet (I've only just begun today), but maybe in there I will find a comment from Alekhine as to Rubinstein's absence from that event.
It tickled my Fischer funny-bone.

I think what's needed is perspective. I looked up Rubinstein's tournament participation in 1923 and found that he didn't play in some major tournaments that year and scored poorly in the ones he did play-
didn't play in:
Hastings 1923-24
Lake Hopatcong in 1923
Kopenhagen 1923
Margate 1923
Scheveningen 1923
Vienna 1923
played in:
Karlsbad 1923, placing 12th
Mahrisch-Ostrau 1923, placing 10th
In 1924 then, he played in:
Berlin in January, placing 2nd behind Johner
Merano in February, placing 3rd behind Grunfeld and Speilmann
The British Championship at Southport in June (I think), Atkins won (I don't know Rubinstein's standing)
Apparently 1923-24 weren't Rubinstein's greatest years for whatever reason and whether this played in his not attending (or possibly not being invited) New York in March-April of 1924 would be speculation or maybe there simply wasn't time, and/or financing, after Merano to make the journey. But it's certainly understandable.
Recently I've begun reading and playing through the 100 games in Rubinstein's Chess Masterpieces, annotated by Hans Kmoch. The games selected for this volume are taken from international tournaments. The earliest tournament cited in this book was in 1907 and the latest was in 1931. What I'm wondering is Why didn't Rubinstein play in the international tournament in New York, 1924? Does anyone know?