The default ssh_askpass program is asking for the passphrase to unlock an SSH private key and does not know about the key ring.

The Gnome Keyring, from what I see, offers an SSH agent. If the key ring daemon is launched at the start of the session then the necessary plumbing (in the form of an SSH_AUTH_SOCK env var) should be in place.

Immediately after logging in...
What are the values of SSH_ASKPASS and/or SSH_AUTH_SOCK environment variables in a default terminal?
Is there a running gnome-keyring-daemon for your user?

If you set SSH_ASKPASS="gnome-keyring-daemon --start" does that help?