What could make a brand new battery die after a few days?

Check the altanator

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you've had the misfortune of getting a bad rebuilt alternator-sorry-they should give you another one -I hope its not hard to replace-Denny

Either a electrical drain or a corroded connection or cable not letting it charge properly.

you likely have some dead cells top up with distilled water
be careful battery acid burns bad....
or replace battery, most places will test your battery for free

If it was an alternator related problem the car would die while it was running. it could still be a bad battery. i have gotten a few new batteries that were bad.

try this:
-drive the car for about 15 mins to make sure the battery has a good charge
-after you park it, then disconnect the (-) neg cable from the battery
-let the car sit over night with the battery disconnected
-the next day hook the (-) neg cable back up to the battery and try to start the car

if the battery is good, it will start normally
if its bad you'll get the -no start- problem

If the battery is good, you have a parasitic drain some where in you electrical system.

it sounds like the battery is bad did you have it checked and just because the alt is new does not mean it is good

have your altinator checked and check to see if your heater core needs to be replace

if the battery holds the charge for a day or 2 wile you drive the car normally then you should check your alternator live the car 2 or 3 days after the battery was charged and check if it starts and run if it does run it another 2 or 3 days and see if the battery dies if it dies most likely your alternator is bad, your mechanic can test it with in 3 minutes to see if it is the alternator or the battery

Never saw an ammeter that had a "normal" reading on the gauge face...You aren't reading the dash gauge are you? Normal procedure is to place an ammeter between the battery and either lead and read draw that way. Then remove each fuse till the draw diminishes substantially. An alternator can draw a bit but it should not be excessive.
Checking charging volts, the meter should not read below about 12.5V even with all accessories on and should not continue to drop regardless of running time. (accessories off reading should be between 13 and 14V).
Also have battery load tested if you haven't done that already just to make sure it is good (even when new) and make sure something simple like a visor mirror light or glove compartment light isn't on all the time.

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