I am finding that in FM12, the Quick Find box stays highlighted and it retains focus (stays active).
The issue I think is why yours is losing focus after the search.
It does not remain in focus from my testing, which in theory should be correct as i am clicking into a field, thus making the field the active object.
The problem is that the information in the quick find is remaining highlighted giving the impression that it is still in focus when it in fact is not.
My apologies. You are correct.
On reread your post, I see that I overlooked your statement that you did click into a field.
I see the issue you are describing. The Quick Find box retains the highlighting for no logical UI reason.
I think you have found a user interface bug.