Thus spake D'Arcy J.M. Cain
> Feb 12 07:26:49 smaug named[22225]: accept: Too many open files
> Feb 12 07:26:49 smaug named[22225]: accept: Too many open files
> Feb 12 07:26:49 smaug named[22225]: ctl_accept: accept: Too many open files

Pardon me for asking a question and then answering it but I found the
problem.  That system is doing virtual domain service and an entire
/24 is aliased to the loopback port.  By default named is listening
on every available interface so it ran out of files.  All I had to do
was add listen-on options for the external IP and the 127.0.0.1 address
and everything seems to have cleared up.

-- 
D'Arcy J.M. Cain <darcy@{druid|vex}.net>   |  Democracy is three wolves
http://www.druid.net/darcy/                |  and a sheep voting on
+1 416 425 1212     (DoD#0082)    (eNTP)   |  what's for dinner.