By lowering the pickup you have reduced the compression on the height adjust springs. You can either put a piece of foam in the bottom of the cavity to stabilize the pickup and make sure your using the correct spring. Stock Gibson springs are pretty strong and depending how low you put the pickup will determine how firm the pickup will be in the mounting ring. Using a pickup without a cover will also cause it to flop around more. If the springs are too loose, the springs can vibrate and generate an unwanted feedback in your guitar.

If you lower the pickup extensively, use a longer spring and one with stronger compression. Pickups with two height adjust screws tend to move around more so having a stronger compression spring should help firm the pickup in the mounting ring.