The sodaq NB-IoT shield is powered by a 3V3 regulator from another board, which is powered by a 5V/1A USB PSU. I also tried a lab PSU at 3V3, with the same results. Never tried 3.7V though.
The strange thing is that everything works fine for 2 hours and 4 or sometimes 5 minutes. If it was a power problem I would expect more random events, not exactly at constant intervals.
Did you notice the problem at the same intervals?
Best regards, Frans.