I didn't read previous posts carefully enough. I see now that the ISP sysadmin says he increased the number of open files limit. But perhaps it wasn't increased enough, or perhaps it was done in a way that wasn't useful to glassfish. Or maybe he just did something wrong and his change had no effect.
It may or may not be helpful, but here's a little script I used to watch my open file count to get an idea of what was really happening.
#!/bin/bash
while true; do
pid=$(ps -A | awk '/java/ && !/awk/ { print $1; }')
ls /proc/$pid/fd | wc -l
sleep 5
done
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