You can try and convert all of your Calibre managed files, to any format and see if any of the books show a problem.
If you don't want to polute your book database, make a copy first and work on that. No guarantee to find the culprit, but not a lot of effort either.
Yes there can be a common cause. The change in hardware does not necessarily mean that there is no bug in the software (even between different versions), that causes this to happen and that is triggered by some (non-standard) sequence in one of your ebooks.
If you have PDF files, it might even be a bug in the program that is part of the PDF file (it can be ...
Could the problem be the charger? Do you still use your old charger with the new Kindle? If the charger is flaky, it could have damaged both Kindles.
Also, it could, of course, just be a coincidence. People's Kindles die all the time. Two dead Kindles isn't really enough to be sure of a trend.
I have a kindle keyboard, and was having similar problems with freezing getting more and more common. I had about 700 different works on it, but it reported it still had lots of room left on the drive. At that time I was getting works from Amazon, Project Gutenberg, Wikisource, and few random places pointed out by Internet Archive. (No pirated works)
It may be that your battery has burst. That would be the most likely cause of an abrupt breakdown. If the device is no longer under warranty, I'd suggest opening it up (check for videos on YouTube) and having a look. Replacement batteries are easily obtainable and, if you can operate a screwdriver, putting one in is within any user's capability.