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Removing a second electron is harder than the first because a net positive charge has already been created. Therefore, the second electron you are trying to remove is being my tightly held by the atom due to the fact that there are more protons and electrons.
The second electron that would be removed is generally closer to the nucleus of an atom. For this reason, it has a stronger pull acting upon it by the nucleus than the first electron does. This stronger pull makes removing the second electron harder.
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