A female convert I know, who had stopped observing mitzvos for a few years, but then sought to return to the fold, was led to believe by someone that she would have to go again to the mikvah to confirm her Jewishness. I had never heard that before and now I have reasons for being suspicious of the advice, given its source. Is this halacha?
...ואפילו חזר ועבד עבודת כוכבים – הרי הוא כישראל מומר שקידושיו קידושין.
ישראל מומר שעשה תשובה – אינו צריך לטבול. רק מדרבנן יש לו לטבול ולקבל עליו דברי חבירות בפני שלושה
...even if the convert returned to worshiping idols -- he is still a Jew such that his marriage proposals are binding.
An apostate Jew who repents -- he does not need to dip [in a Mikva]. Only rabbinicly he should dip [in a Mikva] and accept upon himself words of companionship (?) in front of three [people]. (my translation)
So a custom like that is on the books. But it doesn't mean they aren't Jewish in the meantime. It's a sort of formal "welcome back" ceremony.
You should have her speak to a rabbi to see how her situation compares to this one.
Here's the problem. In theory, conversion is instant and irreversible. If we had a magical machine that could peer into someone's soul so we could be certain that right before the conversion s/he was sincerely committed to keeping everything; then the next day somehow something totally changed and s/he decided to worship idols and eat pork or whatnot, we would call them a Jew who is sinning.
In our normal world, however, we can't always tell whether a convert is entirely sincere, or just how deep their commitment runs. One interpretation of the book of Ruth has Ruth and Orpah converting back in Moab, but it's only Ruth's later declaration (and insistence) that show that her commitment was solid, whereas Orpah's wasn't.
So ... let's say a non-Jewish guy comes in, swearing on a Bible that he came to Judaism "through his Jewish girlfriend, but not because of her." (A dayan involved in geirus said he liked that phrasing.) He converts. The next day, she dumps him. From then on out, he stops keeping shabbos, kashrus, or anything else. This might cause a reasonable person to question whether the initial conversion was really sincere.
So the convert whose observance lapses will always face scrutiny, fair or otherwise, that perhaps the initial commitment wasn't good enough. It thus wouldn't surprise me if some would want to play it safe with another dunk in the mikvah.
(At the same time, please apply some reasonable limits. If someone converted and kept glattkosher/chalav-yisrael/or-zarua-veses/daf-yomi/rabbeinu-tam-zemanim/magen-avraham-krias-shema/gedzundheit for fifty years and then had a lapse in religious observance, we'd say that person changed at some later point!)