The first thing to try is "Keychain Access" menu > "Keychain First Aid". That will offer to check your keychain for problems and possibly fix them.
If that doesn't resolve it, and if you have not explicitly added secure notes, custom certificates, or are otherwise are not even sure what keychain does yet, then there may be an easy solution for you. Just go to Keychain's "Preferences" dialog and click the "Reset Keychain" button. If prompted, allow Keychain to synchronize with your login password. Then, the next time your email application prompts you to enter a password do so and choose to allow Keychain to save it. You may need to do this for both the sending and receiving servers. That should solve the issue. Note that this will move your old keychain aside and create a new "clean" one.
Although that solution is rather generic for all Keychain issues, I have also experienced one specific reason that Keychain will frequently request a password. This occurs if you have created or opened additional keychains other than the default "login" keychain. If you have been playing with keychain and have created a second keychain or opened a keychain copied from another Mac, then try closing that keychain and see if the issue goes away.