Euler's theorem of Rotation for rigid body states that
In three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point.
Intuitively, the axis of rotation can change from $\hat{\textbf{n}}$ to $\hat{\textbf{n}}^\prime$ from one instant $t$ to the next $t^\prime$ in a continuous manner. But the motion need not be such that there is a finite time during which the system maintains a fixed axis. How is it then meaningful to talk about the axis of rotation at a given instant?