I always carry paper copies of anything travel or visa related because I never trust myself to locate anything electronic when I need to. The only exception is boarding passes, where I am content to rely on the electronic version. That said I did recently manage to lose by mobile boarding pass between scanning at the gate and entering the aircraft- it just disappeared from my phone and when I logged back into the App I got the usual BA "not refreshed since 1965" and "We can find no bookings" messages. Thankfully I had remembered my seat number so it didn't end up being an issue.