The problem is in SQL Logs.
Just had the same problem, fixed it by disabling SQL logs.
This is what I have in the process list when this is happening:
After killing these processes the server goes back to normal state, until it is trying to write some other logs.
*EDIT*
Fixed it by converting all tables to InnoDB and then back to MyISAM.
After this the server is working fine after all the restarts made and the logs work too.