Car won't restart after running for more than 10 minutes

Have a 1975 Firebird. It starts when cold and runs fine. However, if I run the car for more than 10 minutes then turn the car off and try to restart it, the starter won't crank enough to restart the car. It's like the battery has gone dead. I end up restarting it by pushing (it's a manual 4 speed) or by jump-starting with another battery. I tested the alternator by removing the negative terminal from the battery while running and the car continued to run strong (actually idled slightly faster without the battery connected). Once the car cools off (after being off for couple of hours), it starts again so the battery seems strong. I'm stumped.