This isnt an answer but a work around. I switched my i5s battery on 10.2 and lost batt stats still have percent working somehow the value for "mah" switched to the %value so it looks like a failing 100/1570mah batt. Every boot i have till min 6 or when i run a semi cpu intensive app before it force restarts without warning. Sound familiar?
I keep an app called system stats (green icon phone with heartbeat monitor line) on my first page which helps me get the timing right it shows the uptime
upon boot i unlock (leaving it locked reboots)
Open system stats>scoll till cpu and the uptime reading are both visable
Open app switcher and swipe all other apps
Return to sys stats cpus should be running high watch it drop to the 60s then 20-30s then 10-20s at this point its around a min-two on uptime
With the system stats still showing i hit power button to sleep
Now you wait
Any notifications that turn on screen just re-sleep phone dont bother clearing or anything. If its an issue enable airplane mode.
Once you are passed 7-9 min you should be ok and your phone wont reset.
Like i said its a work around but it does work getting it to try to deep sleep asap works because iphones post boot if you dont unlock will continue background startup then sleep after the backgrounding time limit is reached which is beyond the 4-6min when it will restart.