Jun 30 20:36:40 web postfix/qmgr: 9BB7E3EC4A0: from=<www-data@SuperWebServer10.superweb.dk>, size=467, nrcpt=1 (queue active)
Jun 30 20:36:40 web amavis: (18021-09) NOTICE: reconnecting in response to: err=2006, HY000, DBD::mysql::st execute failed: MySQL server has gone away at (eval 86) line 166, <GEN117> line 3.
Seems as if there's a problem with your MySQL server. Did you check your syslog for MySQL error? MySQL problems can also originate from not having enough RAM or a high system load.