So, this is more a problem in communication (still a problem, though) .
The value shown in the camping window is your base % chance (it goes up by 1% ever day that you spend in that specific location).
The value given to you after every consecutive battle is in addition to this base number, but is not saved for the next day. So, with these screens as an example, the base search chance is -8% (so zero), and the consecutive battle modifier is 9, pushing the player up to 1%. After your last battle of the day, the game checks to see if you hit the 1% chance, tells you the result, and then promptly forgets your battle modifier ever existed. The increase you see on the camping screen after battle is the daily tick to increase the base percentage.
As I'm writing this, I'm wondering how to better explain the jist of it to the player, and I'm not entirely sure. Part of me wants to use Kermit to just explain things in plain language, but I don't want to over use him. I could potentially add a visual to the search code to physically show the numbers changing and then going away after the end of the fights. I'll think on it some more.