Backup through WHM fails at mysqlcheck

Every time I try to run backup in WHM, either through the nightly automated schedule or manually, it fails when it starts using mysqldump. So I ran mysqlcheck to see if anything is wrong with the database and that's where I found that mysqlcheck will crash MySQL every time. Once the check gets to a big table, the check stops and MySQL restarts itself. I know it's not something wrong with the particular table because the table it stops on is not always the same and I can also use CHECK TABLE on it in phpMyAdmin and it shows that it's fine. Backing up was working fine until recently. My database is a little over 20 GB and the VPS plan I have with my host has 6 GB of dedicated RAM. After looking at it for a while they got back to me and said I will need to upgrade my plan with them because I need more RAM for this to work. Does this sound right or could there be another solution without spending more money?