There is either an intermittent break in a wire, possibly a failing voltage regulator, or there's a defect in the alternator. Was that a professionally-rebuilt alternator from an auto parts store, or a used one from a salvage yard? If it was a used one, I know this is unlikely, but did they tell you how many miles were on the vehicle it came from?
It is also possible the replacement alternator has one failed diode of the six. When that happens, it will only be able to develop exactly one-third of its rated output current. The battery will have to make up the difference as it slowly runs down.
The first step has to be to determine exactly how this is failing. By that, I mean the system could be working normally, then suddenly fail completely. At most, that will let you drive for no more than an hour after that failure starts, and much less if you have the head lights or heater fan on. That type of problem we should be able to find with some voltage measurements, but that has to be done while the problem is occurring. You'll need a test light or a digital voltmeter. Check out these articles, then I can help you with those if necessary, including places to buy them:
https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester
https://www.2carpros.com/articles/how-to-use-a-voltmeter
These measurements must be taken with the engine running.
It's rather difficult to test for a defective diode yourself, and the results can be open to interpretation. Almost all professional charging system testers will measure "ripple voltage" which will be excessive if a diode is defective. Diodes are rarely intermittent, so if they test good, we'll know we have to look somewhere else.
You should be seeing the red "Battery" warning light in the instrument cluster when the problem is occurring. When that turns on, or whether it's on all the time will give us a clue.
We should also start with reading and recording any diagnostic fault codes. Chrysler made doing that yourself much easier than any other manufacturer. Cycle the ignition switch from "off" to "run" three times within five seconds, without cranking the engine. Leave it in "run", then watch the code numbers appear in the odometer display. You can go here:
https://www.2carpros.com/trouble_codes/obd2/p0500
to see the definitions, or I can interpret them for you. Be aware any fault codes will be erased if the battery is disconnected or it runs down too far, then that valuable information will be lost.
Let me know how you'd like to proceed.
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Thursday, February 25th, 2021 AT 5:46 PM