My 2006 Acura TL has had this happen twice now, this is how it plays out:
1.Driving along and the battery light comes on and the transmission shifts rough
2. Then then the air bag light comes on followed by all the warning lights on the dash
3. Then all the gauges die, like the fuel gauge just drops off to 0
4. The car still drives enough to get me to a close location but once I turn it off it is dead. will not start and acts like the battery is dead even though it isnt.

The first time I left it overnight and jumped in the morning and is drove for 4 weeks without an issue.
Tests performed after episode 1:I load tested the battery and it good, put a meter on the alternator and it is pushing 13 plus.
The second time same events. Right now the car is dead.

Going to look at replacing the cables at this point but to be honest they look fine. I have seen posts about ignition switches and sensors causing issues.

Any ideas?

Any idea

 

I had this happen when my alternator was going out on another car. Same symptoms. After replacing it, it worked flawlessly again.

 

Mine acted in a similar manner...it was a bad battery cable.

 

At this age, the + battery cable is likely corroded internally where you can't see. Had similar problems a couple of years ago. Turned out to be that cable.
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it's the battery cable.

 

OP you said your alternator is 13.
alternator should maintain battery voltage between 13.9 and 14.8 volts (14.2 is optimum).

is it within those numbers?

What is the status of your HFL?

 

battery terminal

 

^^^^^
i had to put a new terminal on my positive cable after getting the battery replaced. After cutting off the old terminal and stripping some of the insulation off the ends, I found that there was a lot of corrosion on it, even under the wire insulation. I'm almost thinking I didn't need a battery as it gave no warning it was going.
Drove home from work, turned the car off, went to start it 5 minutes later, only clicking and flashing dash lights.