The problem seems to be (for lack of better information) that sites are shut down pre-emptively with no warning.

I'm all for prosecuting child pornographers, and shutting down their content as quickly as possible - but that should be possible by a court order against the hosting provider.... or if said provider is unreachable / out of jurisdiction, and has STILL had some reasonable attempt at contact to press charges, then sure, go after the domain - but there needs to be some due process behind things rather than just having the federal authorities and DNS layer just whomping things down with little to no oversight.