Tragedy has struck an ’80s-themed Royal Caribbean cruise … the fiancée of Faster Pussycat’s lead singer has died after going overboard, though her body remains missing, TMZ has learned.

Kimberly Burch — fiancée of Faster Pussycat frontman Taime Downe — fell to her death shortly after a heated argument with him aboard the ship, according to Kimberly’s mother.

Carnell Burch tells TMZ … Taime called her on Monday to deliver the heartbreaking news. It’s still unclear whether Kimberly jumped or accidentally fell from the ship, but Carnell is confident Kimberly wouldn’t purposefully hurt herself.

A Royal Caribbean Group spokesperson tells TMZ … “Our crew immediately launched a search and rescue effort, is working with local authorities, and we are providing support and assistance to the guest’s family during this difficult time. To respect the privacy of our guest’s family, we have no additional details to share.”

Kimberly was accompanying Taime Downe and Faster Pussycat, as the band was a featured act on The 80s Cruise — a nostalgia-themed trip that also featured performances from Squeeze, Adam Ant, Tiffany, and Men at Work. The incident reportedly took place on the first day of the 7-day roundtrip, which set off from Miami.

A U.S. Coast Guard spokesperson tells TMZ … the incident happened roughly 20 miles away from Freeport, Bahamas. The Coast Guard deployed a helicopter crew and other personnel to assist the Royal Bahamas Defense Force in their search. The Royal Bahamas Defense Force later suspended search efforts.

Kimberly’s mother tells us she has not spoken to authorities yet, and Kimberly’s family is trying to get ahold of them, as they are looking to recover the body.

We’re told Taime and Kimberly were together for about 6 to 7 years.

Kim was 56.