Another approach is to use the screen
command which can be very useful for this.
First you open your SSH session, then type screen
at the prompt. That opens a new session in which you can run your logstash command.
When it runs, you simply press Ctrl+a d
in order to detach your self from that screen and you can safely logout.
Whenever you log back into your SSH session, you enter screen -r
and you will get back into your previous session where logstash was started.
You can create as many "screens" as you wish to start many different processes at different times.
Also see this comparison between using nohup
and screen