update on Oct 19:
I am still suffering from this. I tried a lot of ways. For instance, I removed the login KeyChain and created a new one. But it can't hold new items inside except I secured WiFi network. All the rest passwords can't be saved here.
I recently updated to the latest macOS Sierra. Though I am not completely sure whether this is the cause, my "login keychain" was totally ruined since then.
Every time I restart my Mac, I got a popup alert like this:
And when I opened the KeyChain App, I got this:
It says it's "Read Only".
Now I have to re-enter every password again (like check my email, log in my StackOverflow account, log in my facebook/twitter). And this happens every time I restart my Mac. It's so annoying. What should I do to fix this?