No need to use the phone browser or the BF app.
Get a $5 wireless dongle for your the pc. (no need on a laptop)
When Internet goes down, flip your phone into Hotspot mode. (not sure about ios but on android it's easy, settings>connection etc)
Change your PC/laptop connection to the wireless hotspot instead of wired.
BA continues as though nothing has happened.
Close your positions.
It's another impressive thing about BA, it copes really well with a change of connection, but your browser might need a restart to reattach.