Help with partial power loss

We currently have lost power to part of our house. The section of the house thst lost power is the basement and 1 upstairs outlet. We have 4 kids 1 being disabled and limited budget. We don't know what to do or possible problem. None of the breakers were tripped. We tried turning main off and turning back on but no results. Local electric company did check everything on their end and outside of the house and things are fine there. They said it might be the neutral in the breaker box. Don't know if this is true or what to expect for an amount to fix this. We had an issue a few days ago where power to this part of the house went out but came back on. But today it went out 6 times and last time it didn't come back on. This part of our house is where our office is and a bedroom. And some of our disabled child's medical supplies charge. Please help. Any advice welcomed