I know what to do... What age are they? ... for every piece .. other than pawns unfortunately :/ make them do 10 push-ups, and if they are like under 10... have them do wall sits, trust me it works ! :D
Anyone got a cure for the chronic piece droppers?
they are 14-17 years old. Funny you mention push-ups. I started them doing that a couple of weeks ago, it's helping a little but hasn't cured it yet.
You could try giving them stress balls. Have them squeeze them whenever they can. This should help with grip. Giving them hard candy that change colors as layers are dissolved can be used as a quick fix until their grip gets better. They will take the candies out to compare and check on them giving them really sticky hands. Another trick that usually works is just sliding the pieces when you move. They have nowhere to fall if you drop them. I feel your pain. Picking up pieces can get so tedious if you have a lot students all at once.
Yep, they and Musikamole can form a support group...

"Dropping like "fall on the floor" or dropping like "what happens after it's hung"?"
This is why real chess terms should be used, except when I am using them. En Prise solves the problem, well, not the problem of hanging pieces. 
Something which might work is to count the captures on the board every time.
This works for me pretty good. Every move I start systematically with this list: 1) look for ideas/patterns, 2) count the captures, 3) look for keyfields and only then I start calculating.
This minimized my blunders to almost zero.
The Heisman mantra of "checks, captures and threats" has helped me be much more consistent. What are your opponent's checks, captures and threats at the beginning of each move, and what are yours?
Right, that's brilliant advice from Heisman, and highly useful.
Note to Gbidari: I've recovered from yesterday! Back to 2000 again (you won't believe just how quickly it happened) Note to others: the guy just smashed hell out of me yesterday night.
I haven't tried it yet, but I have an idea for a 1 on 1 exercise with a student who drops a lot of pieces. Before they move they have to write down what they mink my reply will be. After they move, if they've hung a piece they have to show me the move they wrote down and we can talk about it. If not, then I don't have to see the paper. But they have to do this for every move.
Dunno if this advice will work for kids its hard enuff for adults to do all the time but a "Brute force search" every move of everything your opponent can do after you move (just a 1-ply search) should eliminate a lot of dropped pawns and pieces. Even a brute force search of all your possible moves each turn should uncover any hanging pawns or pieces. But again, this is easier said than done...at least for me
If they keep failing at it, I guess you could force them to record 3 of your possible checks/captures. Then if their move hangs a piece anyway at least you're making them practice the right kind of thinking... hopefully they'd eventually start looking more and more carefully at your forcing moves.
My own method of avoiding one-move blunders has been declared illegal by FIDE.
Instead of making the move on the board and then writing it down, I do it in the opposite order. After deciding on a move I first write it down, then visualize myself making the move on the board (but I don't actually reach out and touch the piece) and then I sit back and relax... as if the move had been made. Quite often, I will spot the blunder at this point... and since I haven't actually made my move yet, I just need to erase the mistake off my score-sheet and re-think the move.
If that moment-of-relaxation doesn't reveal the move to be a blunder, then I reach out and make it on the board.
I'm coaching some kids that keep dropping pieces. Haven't found a cure yet. If you've had any luck curing this problem, I anxiously await your advice.