Before our wedding, a mikvah lady learned that my wife was marrying me -- a convert to Judaism. Her response was that I must represent a "farblondzshet neshama" (a confused or a lost Jewish soul). She said that someone in my family tree must have been a Jew who converted out and now his soul wants to return. In fact, I descend from a Jewish man who immigrated to the American colonies in the 18th century. What is the Jewish source, if any, for the thought that a Jewish neshama can return in a descendant's body and convince the descendant to convert to Judaism?
In a Teshuva of the Maharam MiRottenberg (#19) he writes that the angel in charge of conception chooses souls from a chamber (that needs to be emptied before Moshiach can come) to place in the womb. Sometimes the angel makes a mistake and puts a Jewish soul in a non-Jewish mother, and sometimes the inverse. The Jewish soul goes on to become a convert to Judaism, and the non-Jewish soul goes on to convert out of the Jewish religion.
The Chida in מדבר קדמות speaks about the terminology of גר שנתגייר - a convert who converts (not a non-Jew who converts) and says that this soul was at Mt. Sinai at the giving of the Torah, and it just took a while for it to find its way to the Jewish people.
So the idea isn't precisely that there was necessarily a Jewish ancestor (although that might have been the cause for the situation). I don't remember where, but I saw this connected to the idea that Hashem offered the Torah to all the nations who refused. Each nation as a whole refused, but certain individuals agreed, and their souls were the ones at Mt. Sinai.
Here footnote 72 quotes the two sources for the idea.