Sounds like a bad alternator...

For example... With a cell phone - if you don't charge the cell phone, it will gradually lose the charge on its battery.

So try charging the battery with an automotive battery charger - I bet everything works great for a little while again - until the battery again drains down.

The way to check this is with a voltmeter set on DC volts. What is the battery voltage with the car off? (Should be 12.75 volts or so.)

After starting the car, what is the battery voltage? (Should be 13/14 volts.)

Note the higher voltage with the car started is the alternator charging the battery!

Also because the alternator was just replaced does NOT mean that is not the problem! (Test with a voltmeter to find the problem. Can also be a poor connection to the alternator...)