My laptop has a switch to put the hardware in offline mode. So there is no
ethernet, bluetooth and so on.
I think it would be the same if you have some USB stick for network connection.
When I start Firefox in the offline mode of the laptop and switch it online
afterwards, Firefox doesn't recognize the available network connections or
network interfaces.
It shows the error page that the server at domain example.com could not be
found.
I've to quit and start Firefox again to get it work.

The ping tool on console has no problem in the meantime.

If the laptop has been in online mode during start of Firefox I can put it
offline/online as much as I'd like. This doesn't harm Firefox. 

Maybe it doesn't recognize a change in the network interfaces. So to say if you
would have different network interface cards and switch. But this I couldn't
test.
At least if you have only the local interface during start of Firefox and add
another network interface for Internet connection later on, Firefox will not
recognize this and can not use it.

I would say that this is a bug in network software if you have to restart when
network interfaces change!?