Rabbit ears don't have much surface area exposed to the transmitted signal, hence the induced signal in the lead to the TV is tiny. If this tiny signal is already down at the threshhold of detection of the TV tuner, then subtle changes in the overall "electromagnetic soup" of all emf in the vacinity of the rabbit ears can have a disproportionately large change in the performance of the TV.
Iwire suggests the idea of ballasts that create broad spectrum noise. . .like trying to listen to a single speaker while a crowd around the speaker is also chattering amongst themselves.
I have even had situations where the simple change in the physical configuration of the branch circuit cables have been what has caused the change. The local branch circuit cables will reflect emf and / or cast shadows.
Changing the antenna location, changing to a different antenna, re-orienting the antenna and / or amplifying the antenna is the key.