Battery goes dead, i mean dead.

Have the alternater checked. The voltage regulator may be sticking and leaving an open circuit.

WEll, something is causing the issue.... First, fully charge the battery, then disconnect the negative and put a volt meter or test light in series (between the terminal and the cable). Disable interior lights, and test for draw of current.
Essentially, if the light lights, too much current is being drawn out of the battery. So, you disconnect fuses, and other items until the light goes out. This should help you find the offending component.

IF no light lighting, perhaps the battery itself has issues. Leave it disconnected overnight, and see if it is discharged...If yes, the battery would be suspect.

There are diodes in the alternator that fail and can cause voltage to be drained. Some tests to the alternator fail to reveal the fault. the best test is an Scope, but you can isolate diodes and test with continuity tester.

Any altenator can test good and it can be bad
If you have a volt meter do this
Get the engine running first of all
Set the volt meter to the AC mode instead of the DC mode.
Connect the positive probe to the negative side of the battery

Connect the negative probe to the positive side of the battery

If you receive the same volt reading as you did in the DC test as before the Diode inside the alternator is blown
The diode keeps the current flowing one direction making this a direct current flow

When a diode goes bad the current will reverse which causes the AC mode to kick in. The battery will olny charge in the DC mode only

Well, not necessarily a fuse, but a current draw. You need to find the draw.

Pull the fuse for the interior lights (so you can open doors and not alter your tests) and clock. Take off negative battery cable and put the volt meter or test light in series between batt terminal and cable. If the light lights or volts higer that a couple of volts, disconnect items one at a time and re test.

Start with the alternator, it is the most likely. It has a series of diodes that change current from alternating to DC, when one fails it leaks current. The unit may still charge, but not as well as with good diodes. The only test for diodes is a scope, or take it apart and test them individually. Use ohms and current flow in one direction, reverse test leads and no current. Failed diode will flow or connect in both directions.

Anyways, you will have an answer pretty quick if you test battery current draw and disconnect one system at a time and retest.

You need to pull fuses to see,but it can still be the alternator,with a bad diode allowing the drain,remove the negative battery cable from the battery,then buy a test light,they are cheap,clip one end to the negative battery cable,and touch the tip of the test light to the battery post,and the test light will light up,cause there is a draw on the system,make sure the doors are shut,and the lights are off.Then unplug the connector on the alternator,if the test light light goes off,the alternator is the problem,if not,remove the dome light fuse,and start pulling fuses one,at a time,and putting them back in,as you go,if you pull a fuse,and the test light light goes out,that is the circuit that is drawing the voltage from the battery,leave it out,and hook cable back up,and see what does not work with the fuse still out,and that will be the problem,please rate if this was at all helpful,thank you.

Look for a blown fuse,and look on the starter solenoid on the batter side hook up,there are more than just the battery cable from the battery attached to the post on the solenoid,there are some smaller wires,witch have fusible links on them,pull on them,if they are burned into,they will pull apart like taffy,you can purchase the replacement fusible links at the auto parts store,,NAPA,also check the large wire on the alternator,make sure it shows 12 volts,with key off,if it does not,then it is not connecting to the battery,just add to this wire,another wire,or small cable,and run it to the positive side of the battery.The connection(plug)at the alternator can be at fault also,if all this all checks out fine,then remove the alternator and take it back to have it checked ,and replaced.

the altenator will test fine although if they did not test with a voltmeter on the car reversing the voltmeters probes on the battery I would say the diode is at fault. when a diode goes bad and the battery is fully charged or new the voltage will look fine but the altenator will not charge as it should, a diode keeps the current from reversing which would be called a direct current as all cars have. if the diode is faulty the current will reverse becoming an altenating current a will not produce a charge to the battery

check the battery with a volt meter. Place the probes from the meter inverted which means positive from the meter to negative on the battery and negative from the meter to the positive one the battery. MAKE SURE YOU STE THE METER TO THE DC & NOT TO THE AC MODE BEFORE YOU TURN THE METER ON. Now start the engine and see if a reading shows of 14 - 15 volts. If so the diode is bad in the altenator. The diode suppose to keep the current running only one way. If the current is running both directions the altenator does not charge the battery completely and the battery light will come on this way also

PUT A TEST LIGHT FROM THE GROUND POST OF YOUR BATTERY TO THE GROUND CABLE CLAMP.REMOVE THE CLAMP FROM THE BATTERY AND THE LIGHT WILL LIGHT IF THERE IS A DRAIN.START UNPLUGGING STUFF [START WITH THE ALTERNATOR] AND WHEN YOU GET TO THE DRAW THE LIGHT WILL GO OUT. TRY PULLING FUSES TO NARROW DOWN THE CIRCUT.WHEN THE LIGHT GOES OUT CHECK THE OWNERS MANUAL TO SEE ALL COMPONENTS THAT YOU NEED TO CHECK. MOST OF THE TIME THERE IS A DIODE GONE IN THE ALTERNATER CAUSEING A 4 AMP DRAIN,IT WILL NEED A RECTIFIER PUT IN IT.HOPE THIS HELPS.

if the alternater light is not on the battery.probably has a bad cell