However, my FP2 still reboots every now and then, often connected with a substantial battery loss (easily > 10 percentage points), see the attached screenshot. Did anybody experience this too? What’s going wrong here?
I had the same issue with my own FP2, but I could easily erase the problems. With my FP2 it seemed to happen, when the battery was too loose and did not connect well enough to the phone itself. If this is your case, too, I recommend using https://forum.fairphone.com/t/fp2-reboots-on-mechanical-pressure/23010 . Just take a piece of paper, fold it so that it fits tight on the lower end of your battery into the case and look what happens.
I had many reboots too when I was using Android Lollipop. Now I use the new beta release with Android 6 Marshmallow and I have no more random reboots except one when I started a call. Afterwards I was able to do a call without a reboot.
It is a beta and something can not work when you try to update but it is also available for you. Each person who is interested in this update can post it in this thread.