"We are working through some things," Jennifer Lopez and Alex Rodriguez said in a joint statement on Saturday

Jennifer Lopez and Alex Rodriguez are not giving up on their relationship.

Shortly after the pair issued a joint statement that they are "working through some things" following reports that they had split, a source tells PEOPLE that Lopez and Rodriguez had indeed hit a few bumps in the road in their relationship due to being long distance.

"They were having problems before she left for the Dominican Republic. Filming made it worse because they haven't been able to see each other much in person," the source says. "But they love each other and want to keep working on things."

Lopez, who is currently filming Shotgun Wedding in the Dominican Republic, and Rodriquez got engaged in the Bahamas in March 2019 after dating for two years.

Over the past year, the couple has spent time at home during the pandemic with their blended families — Lopez's 13-year-old twins Maximilian "Max" David and Emme Maribel with Marc Anthony and the former MLB player's daughters Ella, 12, and Natasha, 16, with ex-wife Cynthia Scurtis.

J Lo A Rod relationship
Credit: HECTOR RETAMAL/AFP via Getty

An insider close to the couple previously told PEOPLE of Lopez and Rodriquez: "They never officially broke up and talked about it but are still together. They hit a rough patch. But were not broken up."

The insider added that the speculation that arose last month that Rodriguez had had an affair with Southern Charm's Madison LeCroy "had no bearing on the rough patch at all."

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Alex Rodriguez and Jennifer Lopez
| Credit: Karwai Tang/WireImage

"She's working in the Dominican Republic and he's in Miami so it's tough seeing each other especially with quarantining and COVID," the insider added of Lopez and Rodriguez. "But they want to try to stay together."

A separate source also told PEOPLE, "This was not caused by a third party. Madison [LeCroy] or anyone else. They are working through things."

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Earlier this year, Lopez talked about having to postpone their wedding two times because of the ongoing COVID-19 pandemic.

"We postponed the wedding twice. We had planned what we really, really wanted to do, [but] I don't know if we'll be able to re-create that," the "In the Morning" singer told Elle. "We canceled it, and since then we haven't really talked about it. There's no rush. We want to do it right when we can do it."

For more on where Jennifer Lopez and Alex Rodriguez stand, listen below to the episode of PEOPLE Every Day.

She also shared last month that the two had gone to therapy together.

"I miss being creative and running on 150," Lopez told Allure. "But Alex, of all people, was like, 'I love it. I love being at home. I love doing my Zooms. I love knowing the kids are there, and you're there all the time.' It has been actually really good."

"We got to work on ourselves. We did therapy," she explained. "I think it was really helpful for us in our relationship."