Fisher exact test is valid for hypergeometric sampling.

This means in a table column and row totals are fixed by the design of study.

This is a rare situation and often the sampling is different. So Fisher exact's test does not hold. 

You can have a look at different study designs named Cross Sectional and Case Control whose sampling methods are not hypergeometric sampling to understand the idea.

Hypergeometric sampling is rare, there is a famous Lady tea tasting example.

Attached is a paper link about this subject.

http://www.ncbi.nlm.nih.gov/pubmed/17315184

Hello,

Please check the attached link

Regards

http://functionspace.com/topic/4433/Fisher-Irwin-test