Why is setting open_files_limit making MySQL slow? We noticed that adding open_files_limit in /etc/my.cnf is making server slow.

Reference : What variable(s) to look to maintain MySQL speed of scanning through all database tables while it starts?
Looking back at my answer to your original post, I recommended a value for open_files_limit. Apparently, mysqld saw that 3145728 was the default value deemed safe enough to use. Hopefully, you changed ULIMIT in the OS to match. Otherwise, you will get lots  of table cache issues. 

NOTE: mysqld will try to choose a fair default value for open_files_limit based on the amount of memory available at the time mysqld starts. There is a warning from the MySQL Documentation:


  mysqld may attempt to allocate more than the requested number of descriptors (if they are available), using the values of max_connections and table_open_cache to estimate whether more descriptors will be needed.


Even if you raise innodb_open_files, there is the possibility of caching file handles against the open .ibd files. See Percona's take on it : http://www.mysqlperformanceblog.com/2009/11/18/how-innodb_open_files-affects-performance/. That may also attribute somewhat to the slowness you are experiencing. 

In your accepted answer, you stated you set open_files_limit to 1048570, a value mysqld felt was too low. Removing open_files_limit=1048570 from my.ini simply allowed open_files_limit to be defaulted to 3145728. You could increase it from that value, not lower it.