This is in general just an annoyance because Dropbox is still running in background (you can check this by opening your Dropbox folder and you will see the checkmark icons and the dropbox context menu entry when right-clicking a file - which are only visible when Dropbox is running).
However, I found several forum and blog posts mentioning that
solves the issue or
sudo apt-get install libappindicator1
solves it. I already had libappindicator1 However in reality the latter is obsolete as the nautilus integration is no separate thing any more. So both did not solve the issue for me.
sudo apt-get install nautilus-dropbox
I solved it permanently only by writing a short shell script (which i put into /opt directory):
(mark as executable) and then click on the Ubuntu button on the left upper corner, type "startup" and there add an entry to call that start that shell script /opt/dropboxrestart.sh.
#!/bin/bash sleep 60s dropbox stop && dropbox start -i &