could be the cause of the pump shutting off, then starting back up after a period of being off.
Normally that is caused by the thermal limiter switch turning off the motor when it gets too hot and then when it cools down, it will turn it back on again. Usually a motor will over heat when a bearing goes bad or there is something stuck in the impeller chamber. But given the booster is after the filter, it is probably a bad bearing. Does it make any noise?