ssh-agent fonctionnant avec i3wm continue à demander le mot de passe à chaque git push

J'ai installé Debian testing avec i3wm en utilisant SDDM (Simple Desktop Display Manager) pour le démarrer. Dans l'espace de travail i3, j'ai pu trouver le processus ssh-agent déjà lancé. Cependant, je suis toujours invité à saisir la phrase de passe de ma clé à chaque fois que je fais un git push sur github (le remote est git@github.com:user/repo.git ). Voir ci-dessous pour les détails. Y a-t-il un moyen d'éviter que cela ne se produise ?

J'ai déjà ajouté mon id_rsa à mon ssh-agent.

$ cat /proc/version 
(Linux version 4.1.0-2-amd64 (debian-kernel@lists.debian.org) (gcc version 4.9.3 (Debian 4.9.3-3) ) #1 SMP Debian 4.1.6-1 (2015-08-23))

$ i3 --version
i3 version 4.10.3 (2015-07-30, branch "4.10.3") © 2009-2014 Michael Stapelberg and contributors

$ ssh -V
OpenSSH_6.9p1 Debian-1, OpenSSL 1.0.2d 9 Jul 2015

$ apt-cache info sddm
Package: sddm
Version: 0.11.0-3

J'ai testé avec succès cette connexion SSH avec ssh -v -T git@github.com et ça a l'air bien :

ssh -v -T git@github.com
OpenSSH_6.9p1 Debian-1, OpenSSL 1.0.2d 9 Jul 2015
debug1: Reading configuration data /home/user/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug1: Connecting to github.com [192.30.252.130] port 22.
debug1: Connection established.
debug1: identity file /home/user/.ssh/id_rsa type 1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_rsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_dsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_dsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_ecdsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_ecdsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_ed25519 type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/user/.ssh/id_ed25519-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_6.9p1 Debian-1
debug1: Remote protocol version 2.0, remote software version libssh-0.7.0
debug1: no match: libssh-0.7.0
debug1: Authenticating to github.com:22 as 'git'
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug1: kex: server->client chacha20-poly1305@openssh.com <implicit> none
debug1: kex: client->server chacha20-poly1305@openssh.com <implicit> none
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: ssh-rsa SHA256:nThbg6kXUpJWGl7E1IGOCspRomTxdCARLviKw6E5SY8
debug1: Host 'github.com' is known and matches the RSA host key.
debug1: Found key in /home/user/.ssh/known_hosts:1
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug1: SSH2_MSG_NEWKEYS received
debug1: Roaming not allowed by server
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /home/user/.ssh/id_rsa
debug1: Server accepts key: pkalg ssh-rsa blen 279
Enter passphrase for key '/home/user/.ssh/id_rsa': 
debug1: Authentication succeeded (publickey).
Authenticated to github.com ([192.30.252.130]:22).
debug1: channel 0: new [client-session]
debug1: Entering interactive session.
debug1: Sending environment.
debug1: Sending env LANG = en_US.UTF-8
debug1: client_input_channel_req: channel 0 rtype exit-status reply 0
Hi user! You've successfully authenticated, but GitHub does not provide shell access.
debug1: channel 0: free: client-session, nchannels 1
Transferred: sent 3252, received 1776 bytes, in 0.1 seconds
Bytes per second: sent 59136.9, received 32296.2
debug1: Exit status 1

Et voici la sortie de git remote show origin :

Enter passphrase for key '/home/user/.ssh/id_rsa': 
* remote origin
  Fetch URL: git@github.com:user/repo.git
  Push  URL: git@github.com:user/repo.git
  HEAD branch: master
  Remote branch:
master tracked
  Local branch configured for 'git pull':
master merges with remote master
  Local ref configured for 'git push':
master pushes to master (up to date)