There are two possibilities from the description you give.
The bottom part of the agitator is attached by bolt to the top of the transmission. If the bolt is loose or the splines/teeth are worn out on the agitator or transmission then the bottom part of the transmission might slip.
There is also an upper part of the transmission. See the image below. The upper part of the agitator is driven by a cam, dogs and spring. It is not uncommon for the agitator clutch dogs (part key 5) to strip out. The part key 3 is a kit 285810 that comes with the cam, spring and dogs.
I hope the video is helpful. This makes a great do-it-yourself project. I hope this information helps. You can reply with any additional details or questions for further assistance.
You can view a video of this repair at the following link:
Changing the Dogs