Hard to say what would happen, up to the DM really. If you had a monstrous cohort and your leadership fell below the effective cohort level for the monster cohort, I say you would lose the cohort. With a regular npc recruited through your effective leadership lvl I would just make the npc lose character lvls or just not listen to or do
what you say until your leadership was back up to where it needs to be or was before. Only as a last resort would I make the cohort leave and abandon you. Maybe you losing your leadership score can be worked into the story of your adventure.
Extra followers desert you, finding someone else to work for.
Your cohort might decide to strike out on his own, allowing you to recruit a new one of appropriate level.
If the loss in score seems temporary (say you died and were Raised), maybe the cohort just goes off on a mission until your score for back up (like when you gain a level or get a Restoration).
The rules for followers are to recruit and lead, the rules for cohorts are just to recruit. So a loss of leadership score (note, you still have a leadership score and the leadership feat, so I disagree with LazarX that you have lost the prerequisite) would not affect an existing cohort at all, but could cause you to lose followers.