Lamar Odom and Khloé Kardashian
09/27/2013 at 01:00 PM EDT
Although they may not be celebrating, Khloé Kardashian
and Lamar Odom mark their fourth wedding anniversary on Friday.
Odom's drug and alcohol abuse
has caused problems for the couple, but Kardashian is honoring the marriage vow of supporting one's spouse through good times and bad, and has not given up on the relationship, a source close to the family tells PEOPLE exclusively.
"She still wants to save their marriage; she wants him to get better, but there is a lot to work out," the source says.
"She's taking everything one day at a time and concentrating on herself. Everything with Lamar is very unclear," the source adds.
The source also says that although the couple are now leading separate lives
, Kardashian did not see trouble brewing on the horizon.
"She never thought she would be in this position," the source says. "Two years ago she would have thought they'd be happily married with kids. It's been so hard to carry this secret and try to save not only Lamar but their marriage. It's taken a toll but she's one fierce lady."
Kardashian herself has said she's tough, but not impenetrable
"As much as I wish I were made of steel . . . I'm not," Kardashian Tweeted
on Sept. 1, adding, "I'm pretty damn close to it though hehe."
Reporting by JENNIFER GARCIA