updated 02/26/2014 AT 2:15 PM ET
•originally published 02/26/2014 AT 9:40 AM ET
“Kate and Matt have been on the rocks for some time,” a source close to Hudson tells PEOPLE in the magazine’s new issue. “They’re not in a great place.”
In December, the couple and their 2½-year-old son, Bingham, were together in Australia, where Bellamy’s band, Muse, was playing. They spent Christmas in the U.K. with Bellamy’s family, skipping Hudson’s mom Goldie Hawn’s annual Christmas getaway in Aspen.
Since then, Hudson has been seen out with family and friends – but not Bellamy – in L.A., New York and at the Sundance Film Festival in Park City, Utah, where she promoted her film Wish I Was Here.
On Tuesday night, Hudson showed up solo at Bulgari’s Decades of Glamour bash at L.A.’s Soho House, where she was spotted without her 9-carat engagement ring.
Despite this, the source says the couple “are still living together. Kate is not giving up.”
Reps for the pair did not comment for this story.
Hudson, 34, and Bellamy, 35, met in April 2010 at the Coachella Music Festival in California. Hudson told InStyle in 2011, “Matthew was polite and immediately protective, which for somebody like me who’s all over the place – one minute I’m over here and the next I’m over there – is important.”
She continued: “I wanted to talk to him and be with him all the time. On our first dates we would take long walks and talk the entire day.”
In April 2011, the couple got engaged, and that July, they welcomed son Bingham. (Hudson also has a 10-year-old son, Ryder, with ex-husband Chris Robinson of the Black Crowes.) Since then, the couple have split their time between California and London, where Hudson purchased a home in 2012, and last summer shot her upcoming film Good People.
When asked in January about wedding planning, Hudson told Kelly Ripa and Michael Strahan: “No, I’m planning nothing right now. I’m so busy, we’ve been so busy, and it’s been great. I come from an unconventional family – my parents aren’t married. So there’s a part of me that goes, ‘If I’m going to do it, I’m going to do it right’ So, no. Not anytime soon, no.”
For more on Hudson and Bellamy, pick up the latest issue of PEOPLE, on newsstands Friday.
Reporting by AILI NAHAS