I received this error on my MySQL 5.6.13 slave
[ERROR] Slave SQL: The incident LOST_EVENTS occured on the master. Message: error writing to the binary log, Error_code: 1590

I issued a slave skip counter:

stop slave;
SET GLOBAL SQL_SLAVE_SKIP_COUNTER = 1;
start slave;

Which somewhat fixed the issue, but then I kept running into Duplicate entries for key errors like this:
[Warning] Slave SQL: Could not execute Query event. Detailed error: Duplicate entry '19905692' for key 'PRIMARY';, Error_code: 1062

Since they were duplicate, I kept trying to skip them, but there was no end in sight. I thought this was odd and wondered if somehow MySQL had reset the slave. I don't know what position it stopped in, so I added a line to the MySQL configuration file, my.cnf, to skip the error code 1062, which skips Duplicate entries:
slave-skip-errors = 1062 #Skip duplicate entry

I have Percona tools sync script running daily, which will fix any inconsistencies.

This is how the error went down in the MySQL error log:

I came across a couple of articles after I went through all this which explains a bit more why this error occurs, except it doesn't explain my duplicate key errors:
Granting privileges may break replication in MySQL 5.6.10
Critical MySQL 5.6 bug: GRANTs and replication

I was issuing some GRANTs at the time replication stopped, and I'm sure I issued at least 1 of them incorrectly, so explains why it broke.