The best thing to do is probably to throttle your log processing to non-peak hours. Log rotation is important (at least to clients, if you're the only one on the server it's a personal prefernce) so you probably don't want to disable it outright.
Login to root WHM.
Click on "Statistics Software Configuration"
Click on "Configure Statistic Process Time Schedule".
Check all the boxes corresponding to the hours you DO NOT want cpanellogd to run.
You'll want to make sure you allow enough of a window for logs to completely finish. You'll want to check this area a day after enabling to make sure logs can keep up.