Jepperson, the company that re-badges the DR1000 and the DR8000 as Portable Aviation Information Managers sells a Stylus Tether that attaches the stylus to the cover - but of course, you need to have a cover, and for using the unit in the cover to be your usual way of reading, for it to be a solution. Here's a
link. But if you do use the unit that way I think, in some ways, it is a better solution than housing the stylus in the unit.
Edit: Just noticed it's not a solution for the stylus supplied with the US version, because the stylus with that doesn't have a hole to secure the tether.