I had this problem recently, but only when the phone was very cold (outside in subzero temperatures), and only when the battery was <50%: the charge graph showed the charge dropping discontinuously to zero (and the phone shuts down and refuses to finish rebooting until plugged into the power). A new battery fixed it: I suspect that the battery has two cells in it and after three years one had aged enough that it was dodgy in the cold. (The new battery lasts much longer in general: a definite benefit of Fairphone, given that most phones require complete replacement to do this sort of thing, which is so disruptive, and much more expensive of course.)