Why does each successive ionization of an electron requires a greater amount of energy?

Answer 1

After an electron has been removed from an atom, the effective nuclear charge (the positive nuclear charge that an electron actually feels coming from the nucleus) increases because the number of protons in the nucleus remains the same, whereas the number of electrons balancing that nuclear charge is decreasing due to loss of an electron. Also, the next electron to be removed may be a little closer to the nucleus, making the effective nuclear charge that it feels higher than the effective nuclear charge felt by the first electron that was removed.

Answer 2

Each successive ionization of an electron requires additional energy because each subsequent electron is held with greater force than the preceding one. This is either because of the reduction in radius (getting closer to the nucleus) or because the ion after removal of first electron is more positive. Either way, the attractive force holding each successive electron is greater and so it takes a greater force.