Update: figured it might be something to do with the DB not being correctly upgraded or a WP core update mucking some dependency up. Also noticed the indexed count had been stuck at too low a number for a while.
Deactivated and reactivated the plugin (after clearing the cache and attempting an index rebuild); I got a screen full of WordPress database error "Unknown column 'content' in 'field list' where it was trying to add indexes for keywords.
The next interesting error was this:
httpd: WordPress database error Duplicate key name 'terms' for query CREATE INDEX terms ON wp_bs2ojz_relevanssi (term(20)) made by activate_plugin, do_action('activate_relevanssi/relevanssi.php'), call_user_func_array, relevanssi_install, _relevanssi_install, relevanssi_create_database_tables
And it's not thrown another error yet... Will update if I notice more errors in the logs.