Every point above the Minimum Skill Level is lost. MSL goes up with your character level, and acts as a threshold to jump-start skills. For example - At level 32, the MSL will be 6, if you take 7 points out of a skill, you get 1 points back.

If you choose to specialize a new skill, that skill will automatically start at level 6. Skills may also receive an XP bonus so they can catch up to your other skills.