anything other happening on that machine? Maybe some scheduled Windows maintenance or perhaps a restart? I had a situation where we were debugging reloads not running on first Friday each month only to find that IT was patching and restarting the machine.
I'd start by going through Windows Event Viewer logs to see if there's any lead there.
I have checked the Windows tasks, IT restarts another service but for every day, not just Saturday or Sunday.
Because all tasks did run, I checked the event viewer and discovered that on Monday the distribution service was restarted, which means before that it was not running. However the event viewer didn't have any information about when it stopped and how...
Maybe it was stuck due to low RAM. There's a setting in QlikView which prevents tasks from starting if the RAM usage is >90%. There are other logs in event viewer which could help you confirming this or you can check performance monitor.