Make sure when you are putting you bit in the router you are not bottoming it out. This could keep the bit from being secured. Also make sure your router's depth adjustment is locked.
I just talked to the guy who bought that lift you speak of, and he said he just tightened the lock nut on the locking cam of the Rockler lift and he hasn't had a problem with it.I had a problem like this with a Rockler lift, which relied on a compressed rubber washer to hold the height adjustment. I suggest you also drop a half inch grommet in the collet and bottom the shank on that. Bottoming in the collet itself is not a good idea. What kind of lift are you using?