Shebyly,
It will show as long as there is network activity, such as apps the connect to your network refreshing. Does this happen if you are connected to your cellular network as well? Let's enable AirPlane mode with Wi-Fi off and cellular data set to off to confirm this is happening due to the network. You can also go through your list of Apps that have Background App refresh turned on and turn off the ones you don't need. You can do this by going to Settings > General > Background app refresh.
You can also check your Mail settings and change how often your new emails are being retrieved. You can go to Settings > Mail > Accounts > Fetch New Data.
This would be expected behavior if the symbol stops after turning on AirPlane mode since this mode stops all network activity.
Take care!