After some unlucky try, I decided to restart dovecot, which said:
Restarting IMAP/POP3 mail server: dovecotLast died with error
(see error log for more information): Time just moved backwards by 899 seconds.
This might cause a lot of problems, so I'll just kill myself now.
http://wiki.dovecot.org/TimeMovedBackwards
Which made me realise that I installed ntp because I had some problem with time synchronisation and it got the time back from more than 10 mn, which seem to give a hard time to dovecot.
So if that happen to someone, don't look for way to fix a SASL authentication, just try to restart your dovecot.
Since there is not once a mention of this problem I could find on the web, I hope this one will help people.