I have the problems on a 13.04 32-bit Ubuntu system.
As mentioned before the "sudo sysctl -w fs.file-max=5000000" still gives the error: "socket.error: [Errno 24] Too many open files".

Side note: when it breaks the GUI (Qt) still keeps running without any notification. I expect a notification is desirable.

After a lot of search and a lot of trying I found out that ulimit did the trick for me.
Add to /etc/security/limits.conf:
*                soft    nofile          65535
*                hard    nofile          65535
Reboot.
Start Armory again (now without the socket.error)

On my intel i5 with Ubuntu 13.10 64-bit the problem does not arise, even with the standard (ulimit -n = 1024).

Reference: http://posidev.com/blog/2009/06/04/set-ulimit-parameters-on-ubuntu/

If you have a fix for this and want to run some tests, please let me know.