Sometimes if they are placed at the edge and they walk off, the model gets replaced with a new card. Is there any way to fix this besides readjusting every time they approach the edge of the monitor?

Unfortunately no @avtom
Its the nature of the program in desktop mode and cant be helped.
It makes sense though, its so you have freedom to place them anywhere you want, open windows, task bar etc. Only way to stop it is to catch them before they do.
I actually enjoy the game of catching them before they fall off windows or walk away hahaha.

Better lighting could help the girls see the edges... perhaps some warning signs. :)

I would say just keep them on the relative safety of the desktop bar, but even then sometimes you click and they just jump off and dissapear! :)

Wow,

And I thought I liked to drink beer!!!