What I expect it to do, and what I think it should do, is just include the expression that's currently underway as the most recent entry in the past-searches list rather than wiping it out with a single keystroke. So that I can do something like:
1. starts typing regex
2. Wait, didn't I just search for this yesterday?
3. up arrow for a while
4. Oh, no, that was something else.
5. down arrow back to the bottom
6. continues on regex started in step 1
That said, even having the up and down arrows disabled entirely would be miles better than what happens now.