Randomly shutting off since ios 8

Question

I Have an iPhone 5 that I updated to ios 8 via iTunes the day it was released.  Things seemed to be fine until today.  I was out and about and was surprised I didn't get any calls or messages, so I pulled my phone out of my pocket and it was dead.  I had to hold the power button down for 10 seconds or more and then the apple logo appeared like it was booting up.  It came online but with one weird thing.  It said "Searching..." Next to the LTE badge in the upper right corner.  I was able to go on the Internet so I knew I had signal (AT&T).  My battery was at 72% so I thought oh well maybe it just crashed.  So I put the phone back in my pocket.  Later I grab my phone and it's off again.  I did the same thing as above... It wouldn't turn on with just a button press, but after holding down power for awhile it finally booted up.  Again 72% battery and searching in the upper right.  So today it did this about 5 times.  On my car ride home it did not, though it is plugged in, running pandora and waze, and it was only a 10 min ride.  But I got home and after being home for about 10 min, phone was dead again.
I Booted it back up like above, same issue but battery was 79% now (thanks to the car ride with charger).  Now it's sitting in my dock and I'm going to charge it a little more before going out again.  Any ideas what is wrong with it?  Never had this issue before on ios 7.1.1.  I just did a "reset network settings" and it rebooted so we will see if that helps at all.

Answer 1

Reset network settings didn't fix it.  Did get it charged to 92% in the dock, went for a drive to pick up a pizza I ordered, but when I got back in the car with the Pizza, the phone was off again.
Another weird thing I notice when turning it back on, though it works ok on the cellular LTE network, it says Searching... next to LTE and it says "iPhone requires your passcode after restarting" - it never said that before on IOS 7.1.
I got it up to 100% battery life but it still shut off.  I also had a heck of a time getting it connected to itunes.  It kept showing the apple logo on the iphone, then it would go dark, then it would show the apple logo again, and basically keep doing that.  I got lucky that eventually I got it to turn on and now I'm going to back the whole thing up and try a factory reset and restore.
I don't think its the battery because I replaced that last winter and the issue was different.  Back then it would just die randomly between 35% and 11% and if you went to turn it on it would show the battery icon with the red line indicating "please charge me".  Its not doing that this time around since the new battery (Jan/Feb timeframe).
What else it started doing today, even though IOS 8 was installed the day it was released, was that I was randomly getting popups saying that other programs were using location services in the background and I could continue or go to settings.  I kept that on for most apps but turned it off for some others.  Not sure if thats related but that just started TODAY, the same day that my signal strength meter isn't working and the phone is randomly shutting down.