This sounds like you're not running the RW server on your local machine, right? In this case you have to keep the server running of course (i.e. your dedicated server which runs the RW server), but there is no need to keep your PC online. You can use screen to detach the server process and keep it running in the background. If screen is installed on your server, you can just run the linux_screen.sh script
Yeah, you're right. I am not running it on my local machine. I am running it on a 2GB VPS. I don't want to keep my PC online
The console is the server, ofc it shuts down if you close it. To leave it on you have to leave your PC on at all times there is no way around that unfortunately.
I don't want to leave my PC on all the time. I have a custom rig and I don't like leaving my PC on. I always turn my PC off at night unless I accidentally leave it on and fall asleep or have to download a game overnight.