We had similar problems in 6.3 and 6.3.1. Before losing your mind trying to troubleshoot the problem, you may want to try upgrading to a later version. That could mean either 6.3.2 or 6.4.1. I can confirm we no longer have those issues in 6.4.1, but I can't confirm that for 6.3.2 because we skipped it entirely. But if you take a look at the Release Notes, it describes similar problems with Control Room. We had to restart our app servers periodically before. Now we've been running 6.4.1 for a week or two now without needing a restart and the Schedules have been triggering correctly.
Dave Morris, 3Ci at Southern Company