Thurman and Balazs have called it quits a second time, her rep confirms

Uma Thurman and hotelier Andre Balazs have ended their three-year, on-again, off-again relationship, her rep, Robert Garlock, tells PEOPLE.

“I will confirm that they are no longer a couple,” Garlock said Monday, the day after a source close to the actress told PEOPLE the pair had split.

The breakup of Thurman, 36, and Balazs, 50 – who had begun dating in late 2003 – takes place amid rumors that the couple were planning to wed in the Caribbean this summer.

Just over a year ago, after Thurman appeared solo at the 2006 Oscars, the Kill Bill actress said in a statement that she and Balazs – who owns such properties as New York City’s Mercer Hotel and the Chateau Marmont and the Standard in Los Angeles – had split.

“Unfortunately, it is true,” she said in the March 8, 2006, statement. “But we remain close friends.”

By last fall, however, the two were again more than just friends, and were seen together everywhere from Copenhagen to New York City – which Thurman and her two children with ex-husband Ethan Hawke call home.

Thurman and Hawke were together for six years, until she filed for divorce in 2003.

Thurman is currently filming The Accidental Husband, in which she stars as a talk-radio host who gets into trouble after dishing out love advice.