When the first proton of the dicarboxylic acids are removed, a carboxylic acid group acts as an electron withdrawing group to stabilize the anion generated by deprotonation. When the second proton of these dicarboxylic acids is removed, a carboxylate (not a carboxylic acid) acts as the electron withdrawing group. Because the carboxylate already has a negative charge, it is much less effective at stabilizing the negative charge.
So, while the inductive effect still happens its effect is much less. Furthermore, you have the additional effect of electrostatics discussed in Reply #1 of this thread. Here, the effect of the negative charge makes it harder to remove the second proton from malonic acid because the two carboxylates are very close to each other. This effect ends up outweighing the inductive effect, making it easier to fully deprotonate succinic acid because the negative charges lie farther apart.