You won't get the influence back that you have "spent" on suppressing a faction. Suppressing a faction incurs an ongoing debit from your total influence generation. Think of it as the same as outpost influence burn. If you suppress a faction or establish a outpost it will cost you one influence. One of options available to you when you have selected a faction is to stop suppressing a faction. Select this option to regain the additional one influence a month, that you were originally generating. Likewise promoting a faction costs one influence.