I was losing frisbees at one of my properties and finally may have observed how this happens. I saw my Sim finish her play session with the dog and the frisbee stayed in her hand. It was stuck there and moved with her. If I clicked on her, there was no option to play frisbee. I had her jump in the pool to see if that would free it since I had found a frisbee in the pool one time. It made the frisbee disappear.
Since frisbees cost lifepoints, this is rather unsettling. I've stopped purchasing the expensive frisbees and have a couple of cheaper ones in my inventory now, but cannot afford to keep buying them. Please help!
***Update**** There is a way out of this! Go to another lot and call your Sim over there, then send them home. When you return to your Sim's home lot (where the problem occurred) the frisbee will be on the ground.