Chosen Solution

I am trying to put a new bit in my rotary tool but it keeps falling off when I try to adjust it

The device collet nut, end piece, may be broken. It will need to be replaced. You can check more information here.

Rotary tools use different sized bits. Commonly a Tool like a Dremel uses a 1/4" collet size. A dental tool, such as the one I use, a Emesco jack rabbit uses 7/16" bits. Make sure your bits are the correct size. https://www.pinterest.com/pin/4602820243