Could it be my sewage ejector basin leaking

I have a basement sewage ejector pump. One day, the sewage water overfilled at the outside of the lid of the pit, and the shower water didn't drain any more.
Obviously the sewage ejector pump was not working. But after a couple days, the water was not seen at outside of the lid, and the shower water drained down. After that, I took short shower twice, each about 5 minutes. The shower water drained down and the sewage didn't overfill, even though the pump was still not pumping (each time, I sent my husband watching the ejector pump while I was having a shower). Then a couple of days later, my daughter had a much longer shower, but this time the sewage water overfilled again at the outside of the lid of the sewage ejector basin, and the shower water didn't drain any more. At that time, we found that the electric cord of the pump was unplugged by accident without being noticed by us. After we plugged it in, the pump immediately pumped the sewage water out. That means ever since the first sewage water overfill, the ejector pump was not working. But the sewage ejector pit seemed lowered the water level by itself unless the pit was filled with water too quick. Where did all those sewage water go when the pump was not working? Could it be the sewage pit has cracks or holes to allow the sewage water slowly leaked to the basement underground? That looks very much like the case. If the crack or hole is on the bottom of the basin, even if the pump is working, the sewage water below the pump float level could still leak to the underground of the basement. If that is the case, what damage can it be? Should I open the lid and have a look at the basin to confirm it? Should I have a plumber to check it and fix it?
Thank you very much for your kind input.
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