Cornwall CC, which owns the civilian airport, had been hoping to take over the adjacent RAF St Mawgan site.
But the Civil Aviation Authority refused to licence the new civilian-led operation because the air traffic control facilities were not ready.
It is hoped that work will be completed in time for services to resume before Christmas.
The local MPs have demanded a detailed investigation into what went wrong.
Matthew Taylor, chair of the group, told the local newspaper: "The first priority is to get this sorted out and flights operating again - but once that is achieved, we need a proper examination and clear accountability for exactly what went wrong."
Dan Rogerson, whose constituency includes the airport, added: "This last minute problem, and the resulting temporary closure, is clearly very unhelpful, and especially bad news for affected passengers. Once sorted out we need clear answers about what went wrong.
The MPs have welcomed work by the council to help passengers booked on cancelled flights to reach their destinations by alternative means.