For a few weeks now, my Nexus 4 (Android 5.1.1, stock rom) has occasionally lost the connection to the sim card. It won't have any connection to a network (indicator in the status bar is an empty outline, not just grayed out) and a few seconds later it will show the prompt to enter the sim's pin that normally only gets shown right after boot.
I have tried different sim cards (that work in other phones), the problem lies with the phone.
This primarily happens when mobile data is being used (I originally encountered the problem while playing Pokemon Go). I don't usually use much mobile data, so it might be older, though the problem didn't exist when I bought the phone in early 2013.
It happens more, the lower the battery is. It usually doesn't happen at all if the battery is >~60%. Then, from there it might happen, but after entering the pin it's good for another 10 minutes or so. The lower the battery, the more frequently the pin needs to be entered until at ~20% it will immediately show the prompt again.
The closest I could find on here is this thread, but since other cards show the same problem, it's not that the sim would need to be cleaned and I wouldn't know how to go about cleaning the reader given it's a unibody phone.
Any other ideas as to what could be the problem? Are there any useful log files I could provide?