We can notice that the weight of the particle would never change, so the force due to its weight will be constant. The deciding factor will be the electrostatic force. When we take the particle upwards, the upward electrostatic force will reduce and hence the particle will try to move towards the equilibrium point. When it goes downwards the electrostatic force will increase and hence it will try to move upwards that is towards it equilibrium position. Hence, by definition the point where it was initially at will be the point of stable equilibrium.