I am not much into the idea of time slips, missing time and other such perceptive phenomena, real or imagined, but as for a physical anomaly...well.
Sounds like the Wiki article you linked on LDE's has a good possible theory.
Ducting in the Earth's magnetosphere and ionosphere at low HF frequencies (1-4 MHz). Some similarities with Whistlers.Hypotheses
Whistlers are an interesting phenomena.
Whistlers
So radio waves (EM waves) from electrical discharges (lightning) create signals that are delayed and stretched through the Earth's magnetic field lines.
They undergo dispersion of several thousand kHz due to the slower velocity of the lower frequencies through the plasma environments of the ionosphere and magnetosphere.If the Sun effects the Earth's magnetic field lines via the magnetosphere then it would also play part in the interference of these radio wave's distortions and time delays.
Alternative Hypothesis
Some believe that the aurora activity that follows a solar storm is the source of LDEs.Maybe not a source but a contributing factor. If we were to accelerate a particle (or radio wave in this case) a slight time dilation occurs, the signal slows from our perspective, and a length contraction, singal appears distorted.
The best thing to find would be a data packet with a time stamp BEFORE it was sent.All of these relativistic explinations show that the signal can be slowed, speed up and distorted as seen from the perspective of an observer but not reverse time. We would need more than just a big magnet and a plasma solar flare to do that, I would think...if it were even possible.
