Unfortunately for Rem fans, the blue-haired demon maid will probably be asleep in "Re: Zero" season 2 or maybe even in more upcoming seasons. The first season of "Re: Zero- Kara Hajimeru Isekai Seikatsu" (also known as "Re: Zero - Starting Life in Another World" or simply "Re: Zero") ended on a cliffhanger where Rem just disappeared, but the continuation of the story in the novel series gave some answers.
At the end, "Re: Zero" novel Arc 3, it was revealed that Rem was eaten by Gluttony (his ability is to eat a being's name and existence) and Subaru was the only one who can remember Rem with his ability, "Return by Death." Unfortunately, his savepoint is after Rem's death so he can't go back in time to save her. He later discovered though Rem's comatose body and that she might be revived by defeating Gluttony.
As reported previously, "Re: Zero" season 2 is expected to follow "Re: Zero" novel Arc 4 (volume 10), which starts three days after their battle with the Witch Cult. Subaru and Emilia would go back to the village bringing Rem's unconscious body with them.
However, her situation won't change even until "Re: Zero" Arc 6. Gluttony will only show up in Arc 5, and he is still alive while Rem remains unconscious in Arc 6. Not to mention, it isn't even sure if Rem will really wake up if Gluttony is killed. Another way to save Rem is if Emilia becomes the Queen. They will be able to use the Blood of the Dragon to cure her.
There is no official announcement or release date for "Re: Zero" season 2 yet, but rumors suggest it will focus on the overshadowed heroine, Emilia, as she pursues the throne with the help of Subaru while Rem is still comatose. This will bring the spotlight to Emilia, whose character development has been lagging behind the twins.