For example, the CVR records only about 2 hours of data.
Overwriting important data must be avoided, and thus the recorders should know if a catastrophe has happened. Then they can stop recording (to protect the already recorded data from overwriting), and start signaling the rescue team.
What is the logic used to stop recording?
The CVR and FDR have impact switches to stop recording when they experience high acceleration. In incidents and accidents that don't involve high enough acceleration, the plane remains intact enough for the boxes to be immediately found and switched off manually. In more serious crashes, the boxes stop recording because of the physical destruction of everything but the memory units (only the memory units are built to survive crashes).
In the United States, CVRs and FDRs have a 10 minute (+/- 1 minute) battery requirement to allow any available post-crash voice and data to be recorded, with power removed once a timer limit is reached.
While I'm not familiar with the internals of the FDR, simple circuitry could trigger the timer to start based on current flow from the battery, if not for an acceleration-based impact sensor suggested.
In crash the last two hours before the crash is most important, so the recorder always recording and stopping when the plane crashes either because of crash sensor or simply due to loss of power and input as the wires leading to it are torn by the impact forces is the right thing.
However in some incidents¹ the data would also be useful. When the crew realizes something occurred that needs to be reported as incident, they are supposed to pull the circuit breakers after landing and tell the appropriate safety board to come for the data (which must be done before next flight). Alternatively if the aircraft is equipped with quick access recorder² they can instead preserve those data, which can be done by any maintenance worker, so the plane can be dispatched again.
However sometimes the crew fails to realize they should preserve the data (or fail to report the incident altogether and it may be reported by someone else like another crew, traffic controller, maintenance etc.) and get scolded for it.
¹ Incident is any occurrence in which safety margins were reduced, but nobody was hurt and there was no or only small damage (with damage to engines or landing gear always considered small). The kind of incident where investigators would most want to have CVR and FDR data and don't always get them is TCAS activations (near misses); they generally have ATC voice recordings and radar tracks, which ATC records in much longer loop, but the on-board recorders often get overwritten either before the planes land or because the crews fail to preserve them.
² The quick access recorder is not crash-worthy and not mandatory, but most airliners have it these days. It usually has longer recording loop and records more parameters, but the main advantage is that any mechanic with portable computer can download the data in couple of minutes and the aircraft can be dispatched again instead of waiting for the safety board investigator to come around.
