In magnetic memory devices, logical bits are recorded by selectively setting the magnetization vector of individual magnetic domains either 'up' or 'down'. In such devices, the fastest and most efficient recording method involves precessional switching: when a magnetic field B(p) is applied as a write pulse over a period tau, the magnetization vector precesses about the field until B(p)tau reaches the threshold value at which switching occurs. Increasing the amplitude of the write pulse B(p) might therefore substantially shorten the required switching time tau and allow for faster magnetic recording. Here we use very short pulses of a very high magnetic field to show that under these extreme conditions, precessional switching in magnetic media supporting high bit densities no longer takes place at well-defined field strengths; instead, switching occurs randomly within a wide range of magnetic fields. We attribute this behaviour to a momentary collapse of the ferromagnetic order of the spins under the load of the short and high-field pulse, thus establishing an ultimate limit to the speed of deterministic switching and magnetic recording.