Yes it sounds like power could be the cause of your problems. Let me explain:
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If the red LED on the Pi is blinking, or not illuminated, then your Pi is likely not getting enough power and you will need a better power supply. (“better” meaning more power capacity). Learn About Power Quality on Pi>
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During encryption, the Pi generally consumes a lot of power (its compute intensive to initially encrypt the file system). If the power quality is poor, then the Pi can behave in ways that will slow or completely stall the encryption process:
a) when power quality is marginal, the Pi can reduce its clock speed to reduce power consumption - this slows the encryption process, dramatically
b) when power quality is poor, then Pi can reset, breaking the encryption process entirely.
Try a better power supply, it will likely fix your issues.