I bought the Surface Duo from best buy a month and 5 days ago. about 2 weeks in I had the same issue you are talking about. I put in for a replacement and it arrived on Friday. I didn't set up the new Duo though till yesterday. I started from scratch without a back up to make sure everything was fresh. Did all the updates. Loaded in my accounts and got everything all set up. Worked fine all last night. This morning I jumped in my truck and turned on the wifi hotspot for the first time and then connected the phone to my trucks stereo via bluetooth for the first time. About 25 minutes into my drive I realized my phone was turned off and when I pushed the power button all I got was that sample blinking low battery indicator.
I don't know what the odds of getting the exact same issue with a phone two times especially when this doesn't seem to be a widespread issue. At least that I can tell. My assumption is that somehow connecting the phone via bluetooth to my car stereo (its an ATOTO Android double din unit) or turning on the wifi hotspot somehow screws the phone? I was smart enough to bring my old Note 8 with me today so when I got to work I took the sim card out of my Surface Duo and back into my Note 8. I just got home and finally got the phone to start up. It showed the battery at 100 %. I immediately went into the settings and started a hard reset of everything annnnd part way through the phone screen shut off and the low battery indicator popped up on the left hand screen again. I'm hoping it didn't brick the phone because it crashed once the hard reset process had started.
I've attached photos I took to show what pops up on the screen when the power button is pushed. That symbol flashes on the screen for about 5 seconds then goes away. Same thing when its plugged in but it shows the plugged in symbol. Holding the power button for 1 minute does nothing. Holding the power button and the volume down does nothing. When it does turn on it turns off after only a few minutes.
I wanted to baby this phone so before I even set it up I put on new screen protectors and a back black vinyl sticker on the back to protect it from scratches. If I have to send this one back I am officially out 2 sets of screen protectors and 2 sets of back covers.