Apache HUP restart problems with large KeepAliveTimeout

We have been having consistent problems when we attempt to restart our
Apache web server each night. We are using the standard Redhat
Enterprise Linux 3 distribution (version "Apache/2.0.46 (Red Hat)"). We
send a HUP signal at 23:55 every day in order to rotate the logs. What
happens more often than not is that the server becomes inaccessible for
several minutes, up to 23 minutes as this example shows:

[Sun May 15 23:55:25 2005] [warn] child process 23256 still did not
exit, sending a SIGTERM
[Sun May 15 23:56:32 2005] [warn] child process 23256 still did not
exit, sending a SIGTERM
[Mon May 16 00:01:01 2005] [error] child process 23256 still did not
exit, sending a SIGKILL
[Mon May 16 00:18:54 2005] [notice] SIGHUP received. Attempting to
restart

This problem seemed to have started after I turned on KeepAlive and set
KeepAliveTimeout to 300 seconds. I recently reset it to 60 seconds, and
the problem seems to have gone away.

While I am happy that the problem no longer persists, I do not
understand why the large timeout setting would cause Apache to have
trouble going a HUP restart.

Does anyone have any explanation for this behavior?