A Relevanssi user reported a mystical database problem. After about two minutes of indexing, the server shuts down the indexing. This leaves MySQL queries hanging on the server, causing the site to crash. The only way to get the site back live was to reboot the whole MySQL server.
Eventually, they were able to figure out the problem. It was caused by a server misconfiguration. The innodb_buffer_pool_size was restricted to an absurdly low number and both query_cache and OPcode cache were missing. Once these problems were fixed, Relevanssi indexing started working without problems.