Let us assume at a given location S, we have E=0. When test charge is placed in this location S,
it will not experience any electrostatic force. But when the test charge make any displacement ΔS and move to S+ΔS,
where the field E+ΔE > 0 , it experiences an electrostatic force and is accelerated.
Hence the test charge moves further where the electric field may not be null. This will be repeated and leads to unstable condition.
Example of mid point between two equal charges :-
Let us consider two equal charges are placed at (a,0) and (-a,0) in cartesian coordinate system as shown in figure.
At origin, we have electric field E =0. Hence a test charge placed at O will not experience any force.
If small displacement is made along y-axis, as shown in figure, there is a net force acting on the test charge.
Hence it will be accelerated and moved away from its initial position and become unstable.