Sleeping mysql processes are a way of keeping a database connection alive, which however can often cause performance degradation. If a large number of these processes don't eventually die, MySQL can run out of avaliable connections.
From the mysql processlist, find if there is a specific database and check if there is any problem on it. The particular database may be corrupt or you may even have to check your code to see if it is closing the mysql connections correctly.
Another thing you can do is to modify the 'wait_timeout' setting in your mysql configuration. In you my.cnf file, under [mysqld], edit or add the line as below:
wait_timeout=600
The above may not be a fix, but can be used to kill off sleeping mysql processes after an optimum time period.
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