It was discovered that the Invariance Weakness of the RC4 stream cipher could be used to recover plaintext from a TLS connection, when RC4 encryption is used.

"The Invariance Weakness is an L-shape key pattern in RC4 keys, which once it exists in an RC4 key, preserves part of the state permutation intact throughout the initialization process. This intact part includes the least significant bits of the permutation, when processed by the PRGA algorithm, determines the least significant bits of the allegedly pseudo-random output stream along a long prefix of the stream."

This can lead to significant leakage of plaintext bytes from the ciphertext.

External Reference:

http://www.imperva.com/docs/HIIAttackingSSLwhenusingRC4.pdf