The problem is that on Toshiba website are only Windows drives available because Linux isn’t supported…
I think you should searching for help on some Linux forums. Maybe they can help you find a proper driver for your WLAN card. WLAN cards are used in many different notebooks so I don’t think it’s a Toshiba related properly.
You say that you do get a connection, so it's possibly not a driver issue at all. Regular disconnects are usually caused by one of two issues -
1 - signal is weak. You can check that by moving to a place known to have a strong signal and no interference.
2 - the most common of all is interference. If you have wireless mouse or keyboard, cordless phones, or anything else using wireless, you may find that physically re-arranging things can make a tremendous difference.