Sometimes, when you install a new version of Mac OS like Mac OS Sierra 10.9.4, you run the risk of resetting your Keychain password. When this happens, your Mac can slow down quite a bit as almost every process will trigger your Mac to ask you for your Keychain password. This is particularly the case when your Keychain password is different from your Mac OS password. For more tips that will help you fix various Mac OS Sierra problems and also performance issues, please go to http://www.whyismymacsoslowallofasudden.com.
If you are seeing your Mac ask you for your Keychain password every time you do anything on your Mac, it is time to reset it. Go to the Apple Menu, then applications and then utilities. Then, go to Keychain access settings and reset your password. If you know the new password that you should be using, you can even go to the verify password option and just enter it there, without having to reset the password. Verifying Keychain with the correct password will also help your Mac remember Keychain login when you visit sensitive websites where you want your login user name and password to be remembered. Resetting Keychain might not always give you that privilege.
Anyways, once you have reset or verified your Keychain password, click OK to save the settings. Saving the settings is very important as merely closing the Keychain Access window will not fix your problem. Also, do a restart for good measure to see if your Mac acts normally after a full restart.
If Keychain continues to irritate you with the password prompt problem, you might have to completely disable it by deleting all saved Keychains and then by enabling it again, after creating one. This might mean that you might lose saved information on some websites but then there is no way around a broken Keychain. It is something that you are going to have to endure.