Strange Availability Problem with MySQL
From the MySQL Documentation


Aborted_clients : The number of connections that were aborted because the client died without closing the connection properly. 
Aborted_connects : The number of failed attempts to connect to the MySQL server


From the look of those two status variables:


Aborted_clients : This should make you look over how your clients are disconnecting. If you connect using mysqli_connect(), you should be closing using mysqli_close(). If you are not and just let the connections die on their own, that might be one probable cause.
Aborted_connects : You should check to see what max_connections is set to. It might be too low and connections are failing simply because of reaching this max setting.
You should raise the max_connect_errors and run FLUSH HOSTS; periodically.
You should investigate the other status variables related to connection errors. You might need to get your SysAdmin involved.