I was experiencing the same issue as many of you. The Galaxy s5 was not staying connected to the carphone in my 2014 Toyota Rav4. I didn't have this issue with the previous android I had, so I knew it wasn't the car. I called Verizon after trying different suggestions on this forum and having no success. I was transferred to Samsung (1 -888-987-4357). The rep had me download an app called Smart Tutor and essentially i gave him access to my phone. He opened, deleted, and changed some of the settings. I then tried out the phone. He called me on my cell and we talked about 4 minutes. The call was not interrupted as it had been before. It seems like the problem is fixed. He provided me with his name and number so I can call him if I continue to experience this problem. I'm keeping my fingers crossed..... By the way, I uninstalled the Smart Tutor after we hung up... It was kind of weird watching my phone moved screens on its own 
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