How can I use a different keychain for ssh?

I'd like to be able to use a dedicated 'ssh' keychain for SSH private keys, but can't seem to get it working. I'd like to be able to keep this keychain locked, and unlock it only when I need to SSH into a server. Then, as soon as I lock the keychain, SSH access should be revoked.

Right now, I can enter the private key password and check 'Remember password in my keychain'. But when I try to SSH again after locking the keychain, it prompts for the private key password again. I thought the idea was to prompt for the keychain password to unlock it?