It's an interesting question -- it might seem like an obvious thing to want to do but currently FARR doesn't really have a way to minimize-during-searching. It assumes that when you want it to "go away" you are done searching.
Let me explain why FARR doesn't "want" to minimize during searching -- it's because FARR was never designed to be used to perform searches that take a LONG time. It's whole purpose in life is to be used to find things very quickly.
What this means is that FARR is rarely the only file searching program you will need. You should have a good all purpose file searcher for those times when you need to conduct long searches and filter by file size, date, etc. There are some good ones -- like Agent Ransack
and some good commercial file searchers.
I will take a look into adding this functionality, but let me encourage you to consider limiting FARR to searching for things that can be found very quickly -- like executable programs to launch or for your normal work documents, and use a different program for very long involved searches.