I don't see how a drained battery would have any connection to low alternator output. Did you check the belt as previously mentioned? According to Paul's test below in post 5 you have a bad alternator, or belt is slipping. I would get the alternator tested by someone other than the guy who fixed it, to get a second opinion.

MP

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra