Q: No Service after battery dies iPhone 5

I have an iPhone 5 that frequently falls to "No Service".  It also suffers from powering off at random percentages, usually around 20-30%.

If it powers off due to a drained battery, it will be stuck on "No Service" for approximately 7 reboots.

(This of course is done after I plug it back in and see the battery % is set to something like 27% instead of 1%)

I should note that I can also lose service without the battery dying, but it will happen EVERY time it powers off from the battery draining.

I should also note that at times my phone will display service bars, however people mention that they can't get through.  I then, try to update through the service number, if nothing works, reboot the device.  This usually "trues up" the information read out, to "No Service" ... as if I had lost service, but the phone didn't display properly, so at a glance, it would seem I have service, when I didn't actually.

I run through the normal protocols to attempt to regain service, but it only seems to return after I continue to reboot the device again, and again.

(Things I try every time)

1, Get under Wifi and call service update number

2, Reset network connections and put in my Wifi passwords again

3, Double check with another device (my wife has an SE same service provider)

4, Rebooting (attempting to wait different lengths of time before powering on to see if it matters at all)

5, I'm on the latest OS

6, I have replaced and tested the SIM card(s)

What I'm really looking to find out here, is if it's something mechanical inside the device that is causing this to occur?

(I've also attempted to get my % more accurate by letting it power up to 100% every time before unplugging it, but that seems to have no affect)

Thanks!