To solve this problem, you have to reset your default keychain. Changing login keychain's password does not help. On macOS El Capitan and Sierra, there is no Keychain Access > Keychain First Aid. It should be caused by changing Mac password using 3rd party software. It has bothered me for several weeks on my new Mac. Because of this, you will be prompted to enter a keychain password each time an application requires authentication that your keychain would normally provide. If you change your account's password using your Mac OS X Install disc (or if your network-based account password is changed due to a network admin forcing a password change), your default keychain password (which uses the same initial password as your user account) does not change. This is needed because, as Apple explains it:

Re-enter the newer password in the Verify field, then click OK.In the New Password field, type the password that matches your current account password.If you entered the correct password, a new window appears enter the original password again in the Current Password field.

Type the former password of the account that you are currently logged in to, then click OK.From the Edit menu, choose Change Password for Keychain 'login.'.

If that is the case, for your default keychain to be unlocked automatically when logged in, you'll have to Synchronize your Keychain Access and login passwords. It could be, too, that you've changed your account password without using the Accounts Preferences pane.

If any problems were found, select Repair and click Start again.

Choose Keychain Access > Keychain First Aid.

Locate the Keychain Access application, under /Applications/Utilities.

It sounds as an issue either with the Keychain App.

Mac keeps asking for password update