Are you getting a message from cPanel saying something like ?
check_mysql has determined that there are corrupted database tables .
cPanel & WHM has determined that the following database tables are corrupt:
Error : Table 'roundcube.contacts' doesn't exist
roundcube.identities.
Error : Table 'roundcube.identities' doesn't exist
roundcube.messages
Error : Table 'roundcube.messages' doesn't exist
roundcube.session
Error : Table 'roundcube.session' doesn't exist
The roundcube database on the server might have got corrupt. You can re-generate the database by stopping the MySQL service, moving away the corrupt ones, restarting the service and then moving ahead with updating roundcube :
# /etc/init.d/mysql stop
# mv /var/lib/mysql/roundcube/ var/lib/mysql/roundcube_bk
# /scripts/restartsrv_mysql
# /usr/local/cpanel/bin/update-roundcube --force
Once this is done, you will be able to access roundcube and the databases will be fixed !