My Z3 shuts down as well at about 40% battery. Can restart it somtimes it will boot up to unlock screen. I unlock it and it may run for a second or it may shut back down. Sometimes it wont make it to the unlock screen. It has been updated as well. Very fustrating. Once it get down to about 29% ( After several restarts ) it may stay on till about 10% battery.
It must be very frustrating that your phone is randomly shutting down. We want to assist you in any way possible. To clarify, is there any damage to your device? Are you using the original charger and if so, have you attempted to use an alternate charger?
I have had the same problem. It started at 20 percent battery and then went up to when it was at 70%. Then it would not stay on tell I plugged it in. I went into store and they factory reset it. Before I could get out of store or finish downloading any opening any programs it did it again. They were great and sent me a replacement one. It started shutting off after a month ( right about the time of last update). Sadly this time they seem not to care. First I went to a level one tech on phone. They were great but could not do much. They sent me to a level 2 tech who was so nice but had to kick me upstairs. The level 3 manager was not nice. He blamed it on the apps and that I have a lot. When I pointed out that the reset would of solved that he said you had downloaded one app within five minutes. When I pointed out that I had not opened it and that I do not think it had finished downloading he stopped trying to shame me and switched to well then I can give you half of what you owe on it. He said split the difference. So basically he wanted me to pay more for this phone that has never worked right and then buy another new phone. I was hopping they cared about me since I have been a customer since 2004 and never had any problems. I just wanted that 400 wavied and give them back phone, I was willing to pay for new one but Paul H in Wilmington NC was hostile from the start and blamed me and everyone else. My only hope is that Motorola cares about thier reputation and makes this right.