The only thing I can think of at the moment is because she was on dial-up and now on BB, make sure the computer is set to never dial a connection. If that doesn't work I think probably a few more details are required;
Is her anti virus up to date?
Has she run any anti spy-ware/Trojan removers?
If that all comes up clean, then what Operating system?
And how is she connecting to the Internet e.g. modem, Network Interface Card? Is she using the USB port to connect to the Internet?
Does she get any errors when it disconnects?
Sorry about all the questions, but it might help.