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I believe water is being used and the pressure in the pressure tank falls below the "cut-in" pressure of the switch and when the power comes back, the switch does not close to activate the well pump.
This leads me to suspect that the small tube that runs from the pump to the control box may be clogged. If this tube were clear the points would close as the system lost pressure. You shouldn't have to turn it back on manually. Check the tube and tell me what you find. Good luck and thank you for rating my answer. Tom