In the show they had something of a falling out cause Lapis wanted to run from Earth and Peridot didn't. This resulted in Lapis fucking off for the better part of a season and taking the barn she and Peridot lived in with her, seemingly because she was hurt and wanted to hurt back. Peridot then spent most of season getting over her and the last interaction the two of them had was in the episode where Lapis came back (aired around a year and a half ago).
Said interaction was only 1 sentence from each of them and Lapis' was, not kidding, "hey." They haven't talked or been physical on screen since, despite them being next to each other quite often, which has diminished fans' hopes for confirmation (not that that's stopping it from being the show's most popular ship, mind you).
Far more interesting though is what happened behind the scenes. Basically one of the storyboarders, Zuke, was the only one pushing this ship in the show. She said as much that she was writing them like they were in a romantic relationship, but that the other boarders might not. Eventually what seemed to be her secret blog was discovered, all about Lapidot, all about being a boarder, all sounding like her. Then things started coming out about how her attempts at a queer relationship were "uprooted and destroyed" and about her no longer working on a show. This is lined up with how Lapis left Earth, along with Zuke not being on the show since that episode.
Basically the ship's biggest supporter, the one who was able to give it a legit push in the show, no longer works on the show. The other crew members haven't been poo poo on it, but the loss of Zuke and the way the characters have barely interacted since her departure have significantly hurt it's chances.