Karen Krantzcke, an Australian player of some note, died in 1977 while competing in a tournament (in Florida, I believe). It was a small tournament won by Billi Jean King if I remember correctly, and Krantzcke either won or lost the doubles final, then went out for a run and sufferred cardiac arrest while running.
Maureen Connelly, the great U.S. champion from the 1950s and arguably the best of all time, died of cancer at a very early age, although she was off the tour by then. In fact, her tennis career was ended by a horseriding accident.
Andrea Whitmore Buchanan, a young African-American player, was shot to death in the late 1970s while still playing on the tour. Buchanan had achieved some success on the Avon Futures tour and, I believe, even won a few matches on the main tour and in Grand Slams. She was good friends with BJK, who was devastated by the slaying.
He wasn't a tennis player, but the husband of Elena Pampoulova Wagner (a native Bulgarian who moved to Germany when she married) died while Wagner was still playing tennis.
Same for Scott Draper's wife, Tracy, who died a couple of years ago when Scott was playing the best tennis of his career, had won the Queens tournament and was ranked well inside the top 40 -- maybe higher.
Can't remember any other deaths on either tour. There was the case of Marc Rosset, the Swiss player, who at the last minute backed out of taking a Swiss Air flight home from the U.S. Open; the plane crashed. It was the first time in his career that Rosset had never left town on the day of a Grand Slam loss.
Butch Walts, a strong, hard-serving American player in the late 1970s/early 1980s, had his career curtailed by testicular cancer. He recovered and became a born-again Christian.