When is the generation of an action potential impossible no matter the strength of the stimulus?

The right answer is Refractory period.

At the moment when the action potential is emitted, the fiber being depolarized, it is impossible to depolarize it again. It is, therefore, necessary to wait until the membrane potential returns to a value below the critical threshold in order to be able to excite it again. We are thus led to distinguish two periods that characterize its excitability.
An absolute refractory period: during which any stimulation, even supraliminal, is ineffective since the fiber is already depolarized.
A relative refractory period: during which a second action potential can be omitted provided that the depolarization produced by the excitation reaches the critical threshold, which implies that it is more important since the value of the resting potential has not been restored yet.