Well from the sounds of it (and please correct me if I am wrong) you do get an internet connection, but after a few minutes it drops connection? So I assume, while you are connected, you can successfully connect to web sites and such right? Also you tried to install via "apt-get install firmware-b43-lpphy-installer", while you were connected via wired connection?
(Note: I don't have this particular card) Looking at possible solutions, how far away from the wifi point are you, have you tried using a different channel, make sure you have strong signal?
Fact, Science and the Pursuit of Knowledge. Working to secure your networks from threats; Outside and Within.