Battery test good. alternator test good. But

The only time I've had a problem with an alternator repeatedly failing is due to improper shimming and the pully wasn't aligned with with the cam and crank shaft which in turn put a tweak in the alternator pully and strain on the bearings. I must point out, this was on a 1978 Chev with V belts. The one that failed a week later, did you have it tested to be sure it failed? Same question for the most recent one. If the alternator are not indeed failing, I'l look to either the ECM or the battery cables/wiring from alternator to battery.

Several things need to be checked before an accurate diagnosis can be made, however in general it is most likely your alternator going out OR a bad connection in your alternator/charging circuit wiring.

It's also important to test/verify that you have a good fully charged battery (with no dead cells) before any tests of the charging system. An alternator needs ample battery power into it before it can produce good charging voltage and amps out of it and back into the battery.

If you test the voltage directly out of the alternator's output post/connector (with the output wire disconnected), you will be reading direct alternator voltage output, which should be approx 13.5 to 14 volts, steady. If the voltage is at ~14 volts, then suddenly cycles down to 9 volts (or anything less than 12 volts), then you have a defective alternator.
If the alternator, while isolated, tests out at a constant 13.5 to 14 volts, then the problem is most likely a bad wire or connection in the charging circuit wiring.

There is also the possibility of the battery (how old is it?) shorting out internally, causing the voltage fluctuation. That's why I previously said you need to verify each battery cell is fully charged and good. You can usually test this with a battery hydrometer (if it's not a "sealed" maintenance free battery).

Clean all connections and make sure they are sound on both the battery and alternator. Electricity does not like to flow properly through dirty and poor connections.

If your alternator is not pushing charge at over +13V(sometimes over 14V, all depends) when the engine is running, then it is faulty. Take it back to where you bought it from and exchange for another.

If the alternator is fine whilst running and the battery shows 9V when the engine is stopped, then your battery is not holding the charge and is faulty. Take it back, same as if the alternator were faulty.

By rights, all things being equal, once started, your engine should run without the battery being connected at all, if your alternator is operating correctly. Your battery is only a storage device to initiate engine ignition. They are rated by CCA, which is simply crank power to turn the engine over and start.

alternator seems to be bad check connections if all else is good have the alternator bench tested

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Take it to an Autozone, or similar, and have the alternator tested (they can do it with the alternator in the car).

Something to consider, when running air and other accessories, it's pretty common for the voltage to drop slightly when idling. Just have it tested for piece of mind.

Check the voltage regulator and the alternator.

Interesting!... without diagnosing it myself, I'd say it's the voltage regulator in the alternator... .that is, if YOU ARE SURE the voltage.. 'sure enough it drops and keeps droping'... That's a SURE sign.

SOUND LIKE THE VOLTAGE REGULATOR BUT IT IS JUST AS CHEAP TO REPLACE THE ALTERNETOR

, do a simple test on the charging system...check battery voltage. should be 12v or better. start engine & check volts at idle, no accessories on. volts should read 13.5 -14v. Turn on all accessories(including headlamps on high) volts should drop slightly but should not creep down. Definitely not below 12.5. If voltage drops lower than 12.5, the regulator (in the alternator) is not working. either change regulator or change entire alternator. Alternator drive belt should have sufficient tension so that alternator cannot be turned easily by hand. If it can, check belt tensioner.

pulling the battery post is not a good test.. It can cause a voltage spike which will kill the alternator if it is not already bad. and it causes a spark at the battery which can cause battery to explode!!!! It is not likely a battery will explode but since you have just charged them they will be "gassy",and I have firsthand seen someone have a battery explode in there face it is not pretty!!!!

if your belt is still on it is most likely the alternator