Too many open files AWS

I'm running my application on Amazon, I deployed a version that separates the log files by tenant and date, so at one point my environment did not accept any more requests, bursting an IOException error. >

    29-Mar-2016 11:56:07.939 SEVERE [http-nio-8080-Acceptor-0] org.apache.tomcat.util.net.NioEndpoint$Acceptor.run Socket accept failed
 java.io.IOException: Too many open files
    at sun.nio.ch.ServerSocketChannelImpl.accept0(Native Method)
    at sun.nio.ch.ServerSocketChannelImpl.accept(ServerSocketChannelImpl.java:241)
    at org.apache.tomcat.util.net.NioEndpoint$Acceptor.run(NioEndpoint.java:688)
    at java.lang.Thread.run(Thread.java:745)

Has anyone ever been through this?