If you just replaced an alternator, it wouldn't surprise me if the battery was also done. A dying alternator will gradually kill an older battery, especially if there are a lot of short trips in the driving habits.

I agree with the comments on cleaning and checking the ground cables.

It's easy enough with a meter to check the alternator output, just in case you got a bad rebuilt alternator. Wouldn't be the first.

I highly recommend getting one of the charging system monitors that plugs into the lighter socket.

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Mac
2002 e320 4matic estate│1985 300d│1980 300td
Previous: 1979 & 1982 & 1983 300sd │ 1982 240d

“Let's take a drive into the middle of nowhere with a packet of Marlboro lights and talk about our lives.” ― Joseph Heller, Catch-22