Redirecting output of a program to a rotating file

If I understood your problem, one solution (without modify myprogram.sh) could be:

$ myprogram.sh | while true; do head -10 >> /var/log/httpd/error_log; done

Explaining:

myprogram.sh writes to stdout
We redirect this output to while bash sentence through a pipe |.
while true is an infinite loop that will never end, nor even when myprogram.sh ends which should break the pipe.
In each loop head command is called to append the first 10 lines read from the pipe to the end of current /var/log/httpd/error_log file (that may be different from the last loop because of logrotate).

(You can change the number of lines being written in each loop)

And another way is:

$ myprogram.sh | while read line; do echo "$line" >> /var/log/httpd/error_log; done

That's very similar to the first one, but this ends the loop when myprogram.sh ends or closes it's stdout.
It works line by line instead in groups of lines.

CodeHunter