My rabbi, who is a member of the RCA, said it's not true that a convert who stops keeping Halacha is no longer Jewish. He said it in response to my question about Ivanka Trump and her attendance at the mixed dancing Inaugural Ball on Shabbat. He also said that it violates several Torah prohibitions regarding how we should treat converts to question their Jewishness. Once a qualified Bet Din confirms the conversion, then they are Halachically Jewish and can't stop being Jewish. He said that's what the Shulchan Aruch says.