As noted above the oil operators contracts allow termination on any number of grounds, with little warning.
The 'losses' are going to be largely covered by insurance, that is why it's bought.
Loss of reputation and/or share price does have a real effect and usually one you cannot insure against.
With the oil operators refuse to use them? Of course not. I seem to recall the Jigsaw contract was given to a company that had no aircraft and virtually no personnel - which you might think makes many procurement prerequisites impossible to fulfill.
Only if there was a systemic problem with the company are the oil operators likely to pull out. With the more responsible oil companies that should be addressed much earlier than any incident.
The amazing thing is how static insurance premiums can be in the face of deteriorating accident / incident rates (unlike motoring for instance).