After some re-producings, please see below our conclusions.
In order to display the like popup window properly, your css template must have enough space at the position you have placed our button.
Even, if you add the official like button at this position, the problem will remain the same.
Usefull info: https://developers.facebook.com/docs/reference/plugins/like
Please, do not hesitate to drop us a line for any further assistance.