Literally, "Incessant questioning until the pot cracks". It is just a colorful idiom of exaggeration. 不要让她知道, 否則她会打破沙锅问到底. It is just like in English using "raining like cats and dogs".

打破沙锅问到底 the original sentence is 打破砂锅璺到底. "璺" is "纹“ ，means crack. so the sentence means " the casserole brokn , the cracks got to the bottom." If you want to know why we say it like this . just remmember : China's food culture penetrates into many aspects of Chinese culture..

It comes from a play on words. “问” puns “纹”, which is the crack at the bottom of a broken “砂锅”. A decent broken 砂锅 tends to have “纹/问” all the way to the bottom.

This information might be a bit long, but i think it's quite helpful for this question. http://iask.sina.com.cn/b/16950147.html