Keychain Password Box Won't Stop Popping UP

My Macbook Air running 10.9.5 experienced some water damage but after a year of sitting dormant, it's back up and running - everything works perfectly.

Except that a box continually pops up asking me to type in my keychain password. Which I do every time - if I don't I can't continue working on my computer.

I have opened my Keychain Access to try and get it to remember it but no dice. I am considering a re-install of my OS but would like to avoid it if I can - because everything else is working fine. This is different than iCloud keychain, I think - because I have that working between my devices.

Any expert moves I am missing? Many thanks.