craft_searchindex table keeps crashing
TL/DR: MySQL is horrible.

The craft_searchindex table is the only table that uses MySQL's older MyISAM storage engine, instead of InnoDB (like the rest of the tables), because InnoDB didn't add support for MySQL's full text search capabilities until very recently (version 5.6.4).

One of the many drawbacks of the MyISAM storage engine, as you've discovered, is that the tables using it can crash easily.  The crashes can occur for a variety of reasons... low disk space, firmware issues, buggy MySQL, sudden server reboot, etc.

From the command line, you can run a "repair all" like so:

mysqlrepair -A --auto-repair
mysqlrepair -A -o


Or start a test that might help you diagnose why it's crashing:

mysqlrepair -A -c


Also, if you know you're running > MySQL 5.6.4 across all of your environments, you can change the storage engine for that table from MyISAM to InnoDB.