Is it common for the snare lug closest to your stick to continually go loose while playing? I play on a new DW and still cant get the lug to stay tight.

Never had a problem with it or heard of anyone other than yourself having a problem, so I would have to say it is uncommon. Try some removable threadlock or teflon tape and that should take care of it.

It happens all the time and is a common problem. You can put a lug lock on it or use 1DrumBum's suggestion and use some sort of removable threadlock. You don't want it too tight or it will be too difficult to change heads.

You might also try changing it out with one of the other lugs. That sometimes works.