Limitations
There are certain scenarios where Independent Component Analysis (ICA) might not work well:
If our unmixing matrix W is multiplied by a permutation matrix P, there is no way for us to know about it. In this case we won't be able to know which signal was from which source.If a row in the unmixing matrix W is scaled by a constant α, this will just result in the corresponding source being scaled by 1/α. There is no way for us to know if scaling has occurred. Therefore, we won't be able to retrieve the true amplitude of our signal.If the data x follows a gaussian distribution, then our sources s will also follow a gaussian distribution. And gaussian distributions are symmetric in nature. Therefore, if our unmixing matrix W is multiplied by a rotation or reflection matrix R, there is no way for us to know about it. Moreover, we have assumed that our data points are independent and identically distributed. This is however, not true for time-series data.
Despite all these limitations, ICA still works very well given enough data.