The reason it clears fields when going back is because php pages are not cached (supposed to be dynamically generated).
However the search form does not change often (only when adding new categories, which happens once every few moons), so I could force to cache it for some time (like what is done for pictures, hence why forcing refresh is needed after replacing a picture).
To change something in the search I usually modify it in the parameters of the page address, but it would be easier to simply use the back function
I'll see if I can do that easily.