My background is in managed intensive grazing. The rule of thumb in the grazing community is "take half, leave half." What that means, is no matter the height of the pasture that you are clipping, you should always leave half of the forage.
I have heard so many people say, "Oh, i clip short and the clover plot still grows back." My answer to that is we are trying to grow as much tonnage of forage per acre per year. The lower you cut anything towards the ground, the slower the recovery time.
Here is a chart showing the effects of clipping your plots too low. Note that if you take 70% of the forage or more, you are really shutting down the plants.
On a side note, the best time to clip your forages is in the late vegetative stage or early bud stage, right before your forages begin to flower.