Jessica Simpson and John Mayer Split

Jessica Simpson and John Mayer have ended their romance – but perhaps not for good, a source close to Simpson tells PEOPLE.

"They have broken up," says the source. "But they have broken up and gotten back together at least ten times before."

According to the source, the pair are in constant contact – even as Simpson promotes her film Major Movie Star at the Cannes Film Festival in France. "They talk to each other at least six times a day. I don't know if this breakup is permanent, but for right now they are broken up."

In fact, the pair have "been emailing and talking to each other," since Simpson went to Cannes, says a Simpson friend. "I'm sure they'll get back together."