Yes the clay sucks the infection out of the gum and if you'll notice after awhile the clay starts smelling terrible because of it. Just take it out and put in more till the abscess is totally gone.
I wouldn't use it constantly because clay doesn't care what it absorbs. It gets everything in it's path, and therefore would harm the mouths bacterial balance. Not a good idea. Oil pulling with coconut oil would give you more than enough anti-bacterial support for daily use.
Even coconut oil I won't use every day for long periods of time.