Did Emile Durkheim have many critics on his suicde theory?
The simple answer to your question is "yes." Durkheim did have many critics on his suicide theory. This is not surprising based upon the fact that he theory was grounded in religious theology.
Durkheim was basically stating his ideology on the suicide rates only using Protestants and Catholics. What Durkheim decided was that the social control which Catholics held over their members insured lower suicide rates.
It was no surprise that his findings procured much criticism. Many found that his findings were simply too generalized and too culturally specific (German speaking Europeans).
Critics, such as Gibbs, Johnson, and Inkeles, have found that Durkheim's focus upon groups and not individuals caused his research to be slanted. (Durkheim, though, did examine the individual. Unfortunately, simply within the constraints of a larger group.)