I also have an HTC One M7. Verizon. I have done quite a bit of research on the issue as well. The problem is 4.4.2. Many phones have had the issue and the One is one of the phones that's still waiting for a fix. I found a bulletin somewhere that said the M7 and M8 would have 4.4.3 available sometime in May to fix the Bluetooth and battery issues that a lot of users are still experiencing. I'll try to find the website again.
My phone was working perfectly fine through bluetooth from when I bought the car in october all the way until I updated my phone in February. Ever since then I have the reconnect issue where it will reconnect itself ever 3-5 minutes.
Edit: Here is one of the links. There are several others too.
http://www.gottabemobile.com/2014/05...rumor-roundup/