Could possibly be the alternator. A friend of mine had a similar problem a few years ago where his car would shut down when the transmission shifted gears. Since the computer in his car required battery power to facilitate the shift and the alternator wasn't charging his battery fast enough, the car just shut down. I would get a second opinion before getting a new alt though.
Other reasons a car may not start all the time could be a bad fuel pump or clogged fuel filter. My Cavalier had almost the same problem and it was the fuel pump, but if your car is consistently shutting down at 50 and not at other speeds, than the fuel pump is unlikely. But if your car will not start, try punching the bottom of your gas tank (this is where your fuel pump is located) and then try starting it again. If you are missing a gas cap or there is a lot of dirt in your gas tank, this will burn your pump out very quickly.