2012 intermittently won't start, irregular alarm sounds

Link to video showing behavior:

Does anyone have a clue what could cause this type of behavior? Every once in a while the alarm goes off when I try to start the car after being locked. Notice the strange pattern of the alarm sound. When this happens, the alarm cannot be stopped by turning the key, pressing the button on the key fob, or inserting the key in the door. However, if I lock the car, walk away for an hour or two and come back, the car usually will start up just fine. Other times, if I put the charger on the battery overnight, it will work in the morning. Other times, it seems like I can start it using the remote start button on the key fob.

Of course the stealership will happily keep collecting my money, but won't do anything to figure out what's going on. First they told me I had something miswired (which could only be their fault since no one else has serviced the vehicle). After they "fixed" that, I noticed that the tone of the alarm changed slightly when it beeps when locking the car. Not sure if that's related but seems like it could be. The next time I took it in, they told me I had a bad battery so I had them replace it, but it has since happened again several times. I have another appointment for it this week, but I'm hesitant to shuck out more cash for more BS answers. Any ideas?