As far as I can tell, only one tennis player in history never had a losing record against any opponent they played more than once. Can you name that player?
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Steffi Graf. No losing records, but a 9-9 split against Martina.
Bjorn Borg game close. If I changed the question to “against any opponent they played more than three times,” Borg would qualify, but as it is written, no. He faced obscure Bob Gerken three times and lost two. Borg was less than 18 years old at the time. (He tied McEnroe 7–7.)
It’s a tough achievement because players lose matches if they are too young at the beginning of their careers (like Borg), and they lose matches if they keep playing when they are fading.

Rafa!
Djokovic is the most prominent player with a winning head-to-head record against Rafael Nadal, leading their historic rivalry 31–29. Among players who have faced Nadal at least five times, Nikolay Davydenko (6–5) and Borna Coric (3–2) also hold winning records against him
Graff was my guess. Can’t prove it because I’m reading this after the answer was posted. She was a machine and generally the first player I think of when these types of questions come up.
Regarding the recent Big Three, I find it interesting how much Djokovic has them beat head to head in major categories. He has the head to head over Nadal and Federer, more Grand Slams and more Tour Titles.