This is unfortunatly not a phex bug. If it would, it would be fixable.
And this is not limited to the search field. About any object in any swing application under unix can be killed. Other OS seams to handle the alternate key different and don't suffer from this. To check it out Yourself:
-Open phex and an other app.
-Focus a component (for example the search field)
-use mouse to select other app.
-use alt+tab to switch back to phex. Hold alt.
-hold alt and press Q to open a query menu. Or just release both and press tab.
Now the previous selected field has still the focus but is inactive.
It's possible to kill even the focus of buttons and checkboxes but this doesn't hurt as much since they are still useable.
This is a known bug in java and will be fixed with release 1.4.
Tha only advice I have about this: avoid the alt key when working with phex.
When someone can reproduce this and does find a swing application that is under an open source license and has a workaround for this bug please post here.
Alexander