Max, one of the answers would be to save the cost of taking the firm private again (buying each other out would be very pricey). You also have to consider the exit strategies from coming off the NYSE (or any other exchange for that matter) of the PE owners which almost always will end in another IPO. With IPOs being priced at 3-5% of the value of the company as the bankers fee or a flat fee equivalent, it's not surprising that remaining listed is the best of a bad bunch.
I heartily agree that having ones name dragged along through the mud is sad to see every quarter but is the price for CHC as a company to pay for having largely discredited former management and reckless owners.