Has there been any cryptanalysis of RC4-52? Several websites ( such as Is there a secure cryptosystem that can be performed mentally? ) briefly mention RC4-52 as a modification of standard RC4.

RC4-52 has only with 52 instead of 256 elements in the state array, so encryption or decryption (or both) can more easily be executed manually (literally "by hand") with a standard deck of playing cards, far away from any computer.
Some people seem to think that, unlike classical ciphers, RC4-52 is difficult to decrypt even using computer assistance.

Has anyone done any cryptanalysis on RC4-52?
Where can I find such cryptanalysis?
A published thesis or magazine article would be nice, but I'd be happy with a well-written blog post.
Well, I have unaware of any specific analysis of RC4-52.  The closest thing I can think of is Cryptanalysis of RC4-like ciphers, which is an early paper which explores RC4.  Of particular interest would be section 5 (Tracking analysis), along with Table 4; that explores the obvious way to attack RC4-52.  Now, I suspect that it could be improved modestly (say, by attempting to search for a Fortuitous State, see section 5), however I suspect that won't gain you all that much unless you have huge amounts of keystream available).