In gnome-shell (and in contrast to Ubuntu), notifications are persistent by default - they don’t go away until you dismiss them.

I have been using notify-send for some time to pop up quick messages that do not need to stick around, so I’m happy to have found how you can make individual notifications transient. If you want to make a transient notify-send message, you can do the following:

notify-send --hint=int:transient:1 [standard-arguments ...]

I’ve created a notify-send script in my ~/bin directory that sets this by default, although that depends on you having added ~/bin before /usr/bin in your $PATH