Why does a reduced compound become a better electron donor? When a compound gains an electron, why are they more likely to give them up (i.e. become stronger reducing agents)?
Simple electrostatic repulsion can be used to explain this. For example, if you have $\ce{O^2-}$, there are 8 protons in the nucleus, but 10 electrons, so there is a net negative charge of 2. Like charges repel, pushing the electrons away.

BTW, compounds rarely "gain an electron", the reactive species are usually radicals.