It sounds like classic user error, saed87. Make sure you only commit a move with the submit move button setting on. Sounds easy eh?
Slippery Pieces

How long since you've cleared your browser's cache? That solves a lot of problems around here, maybe we'll get lucky and it will solve yours too. Here are the instructions for Chrome, but there are articles for Firefox and Explorer as well.
https://support.chess.com/customer/portal/articles/1731819
Oh I just delete the cached images and files and leave the other stuff unchecked. Good luck!

That will also happen when your mouse's left trigger/button starts wearing out. You won't notice it anywhere else except in something like a chess game, because your mouse still 'clicks' fine, it's only when you are trying to 'hold something' for a few secs, the mouse will let it go.
At first it'll only happen here and there, but, if it is your mouse, it will get worse, and worse, and become obvious.
I have the same problem with slips on my laptop mouse pad. My solution is to click and highlight the square of the piece that i want to move, then click on the square that I want to move it to.

The best way not to mis-make a move is to use analyse...won't help you make the best move, but it does lessen uncertain ones....stop blaming the buttons. It's a machine, you input.
Today I started experiencing this, pieces slip when I want to move them, if I want to move my queen from a1 to a8 for example, it stops on a4... I lost many games today because of this and I don't think it's my mouse... any ideas?