Are there currently or have there been historically orthodox female kabbalists? If not is this a quirk of history or is there a specific reason?
Chabad.org has an article by Yael Levine Katz about three women with connections to Tzfas (Safed) that either were kabbalists, or exhibited kabbalist-like characteristics.
Francesa Sarah mentioned by R' Chaim Vital, was said to have had a maggid, or angelic tutor.
Channah Rochel Werbemacher or "The Maiden of Ludmir" who gathered something of a Chassidic following.
Because the article focuses on Tzfas, it does not include other similar figures. For example Udel, the daughter of the Baal Shem Tov, also become something of a female Rebbe after her father's passing.
Another was Rachel Aberlin, also mentioned by R' Chaim Vital, in the same book as Francesa Sarah.
This page discusses some of these women, as well as an unnamed woman, mentioned as "the daughter of Rav Raphael Anav", who was influential in her community.
Much of the history here seems sparse, and one of the main reasons that they (as well as other female kabbalists), might not be well known is that they don't appear to have authored any books.
With few exceptions, kabbalists are known and remembered because of the works they create. The notable exception would be the Arizal, whose many students' many works did that for him. The more influential their works, the more famous they become, and the more prominently they are remembered by history.
For a more contemporary example I would include Yemima Avital founder of the Yemima school.
for an overview see this paper, particularly starting on page 199 for description of connection to kabbalah.
This video lists 10 Jewish traditional female mystics (most not included in other answers)
Inés of Herrera | The Child Martyr | 1488-1500
Fioretta of Modena | The Kabbalist Bubbe | 1522-1580
Asenath Barzani | The Kurdish Rosh Yeshiva | 1590-1670
Francesa Sarah | The Maggid Whisperer | 16th Century
Daughter of Anav | The Oracle | 16th Century
Rachel Aberlin | The Patron | 16th Century
Sonadora | The Dreamer | 16th Century
Eva Frank | The Queen Messiah | 1754-1816
The Daughter of Joseph | The Redeemer | 12th Century
Sicilian Prophetess | The Pregnant Messiah
The Maiden of Ludmir | The Hasidic Rebbe | 1805-1888
Hasidic Women | Odel the Daughter of the Baal Shem | 1720 -1787
Etty Hillesum | The Diarist of Heaven and Hell | 1914–1943