That's a unique issue. I have fixed a dozen or more Reeflo pumps. It would be an electrical issue, most likely a faulty connection or component. I'll be in town next Tuesday through Friday and would be happy to come look at it then. In the meantime, I have a few suggestions:
While it's running,
1. wiggle/reposition the plug in the wall to see if that is the cause,
2. wiggle the cord at the pump to see if that causes the interruption,
3. wiggle the cord all over.

4. put your nose down by the motor to smell or hear any sparking.
After running, unplug the power cord and put your hand on the capacitor component, the box on the side of the motor, to see if it is really hot or actually cool to the touch.
That's all I can think of for now. After doing the things above, feel free to call me at 808-345-1049 for more troubleshooting help.
Aloha,
Mark
