Most probably your app is printing to standard out (the console), and that stream is closed/broken, when you put your laptop to sleep.
There are at least two options:
Use screen: Just type
screen
before starting your app. Then start your app. Then Ctrl-A-D to detach from the screen. You can then safely log out from the VPS and put your laptop to sleep. To go back to the output of your app, log back in and typescreen -r
Run the app in the background:
node app.js &
.