Why do indexes in tables break when backing up a database?

Question

MySQL

We have a dedik from 1dedic.ru Backup
(boxed in ispmgr) starts at 7 am. Sometimes at the start of a backup, errors about broken indexes in tables immediately begin to fall.
Every time the problem occurs with the same tables.
The base weighs about 300mb.
Backups were transferred to different times (night, morning, evening) - the indexes beat clearly during backup.
Where to dig? The hoster says that everything is in order with the disk and memory.

Answer 1

How is a backup made? table lock and rsync/snapshot, binary dump like xtrabackup, mysqldump or alternative method? Yes, I would like to see errors.

Answer 2

for the time of a backup I hope work the database stops?? write cache is reset??
Online database backup is more complicated than just copying files :)