Eventually one of these private space companies will have a highly public, challenger-type disaster. I wonder if a startup like SpaceX could survive something like that.
If SpaceX has 500 successful launches and one blows up and kills everyone on board, it will be sad, but it wont kill them, it might not even hurt their stock if they couldn't have avoided it.
That is a long way of saying the answer is that they probably won't have an issue if they have done a good job on the engineering and find out quickly the root cause of the accident.