Most drivers that you have had for quite awhile are at a level higher than your own. For example you are level 10 but your driver is level 12. That means the search tool will not show you that driver if it is returned to the driver pool. There is no way to get such a driver back as far as I know.
Clicking on team/drivers will allow selection of a previous driver without having to go into search.
I think previous drivers are a special case and not subject to the level restriction. I see you've had quite a turbulent relationship with poor Grace :-) Is it to keep wages down?