I think I may have solved my Kindle Fire 7 HDX autonomous reboot problem: Product: Kindle Fire 7 HDX 3rd generation Software Load: Fire OS 4.5.5.2 – Installed in September of 2016. When I check for updates this is the latest. Case: No case has ever been on my Kindle, so case is not an issue.
https://www.amazon.com/Fire-Tablet-HDX-7-Previous-Generation/dp/B00BWYQ9YE

