[CentOS] Logrotate Issue

I keep logfiles for each of our hosted domains in their root/logs directory. Each month, logrotate runs but fails to recreate the logfiles after this rotation. I've noted that a restart of Apache fixes this. The issue is Webalizer doesn't have log files to work from for a day to several days depending on whatever the heck it is that seems to recreate them like on Sunday following the start of a new month.

Perhaps my storage of the logs in a 'semi-non-standard' location is causing this? I sure would like to have some input into a best solution. I really don't like automatic restarts of Apache, but if there is no other option, I'll do that. Anybody had this issue and come up with a good cure?

Thanks, John Hinton