Problem with alternator failures for 2007 Honda Accord EX

[baskervi]

My daughter has a 2007 Accord EX, and the alternator went out a little over a year ago. I replaced it with an AutoZone Duralast alternator and replaced the battery. At around 3 months, she called me while driving and said smoke was coming out from the engine area. It turned out the alternator was about to catch on fire. I'm 10 hours away, so she had a local person replace the alternator with the warrantied Duralast. A few months ago, she started having problems with the car dying while driving down the road and also be dead in the mornings. It was taking constant charging of the battery. She took it into a couple auto part stores and Walmart, and they all said the battery was bad. The day after the battery was installed, it was dead again. I finally went there with my tools, and noted the battery would start off around 12.4 V, which is low, but would drop to around 11.5 V when the car was started. I replaced the alternator again, so it's been working for a while.

She just called me again. Last night, the interior lights were flicking when the car was off but the door open. Today, the battery was dead again. I've asked her to get the battery charged and give me a call to read some voltages and check what the current draw is at when the key is out of the ignition. 

Given she lives 10 hours away, but is somewhat mechanical and is pretty easy to walk through remote troubleshooting, can something think of other things to check? I presume with the alternator failures, something is drawing excessive current. I'm not blaming the Duralast alternators. I could see getting one bad, but not 3 within a year. I need to find the root cause, so I'd appreciate all ideas.

Thanks