Fail to separate sound signals by FastICA on real-world recording
ICA in raw form is only suitable for use with phase synchronised observation mixtures. Using microphones as you have described will introduce a phase delay as pointed out by other posters. However this phase delay can be used to great avail. The best known algorithm that deals with stereo separation in the presence of delays is DUET. The links are broken but the references you are looking for are here >http://eleceng.ucd.ie/~srickard/bss.html. 

This is the paper you should look for > 
A. Jourjine, S. Rickard, and O. Yilmaz, Blind Separation of Disjoint Orthogonal Signals: Demixing N Sources from 2 Mixtures, IEEE Conference on Acoustics, Speech, and Signal Processing (ICASSP2000), Volume 5, Pages 2985-2988, Istanbul, Turkey, June 2000