It sounds as if the scheduler (the little icon in the system tray) is not switched on. Every time you start CRD, the scheduler starts again. So your schedules will go. You need to make sure that the scheduler is left switched on when you go home on Friday. That's what is important, and not the Editor.
If the scheduler is bombig out sometime over the weekend, then you need to look in the error log to see if you can identify what is causing it to do that. Perhaps if you log a call with CRD support they will be able to help you identify what is causing the interruption.
The icon is showing in the task bar. I leave the application running so maybe that is why. I don't see anything in event logs or the CRD error logs. I'm stumped. As for the call to support... I've been told they do not offer phone support. Everything is done through email, which is a pain in the neck IMO. It takes days just to have quick conversation since I'm in the US and the support is in the UK.
My experience of their support is quite different. I simply go to Help - Support - Technical Support and fill in the form and they usually get back to me within half an hour if not sooner with an answer - and I am on the West Coast!
I don't think leaving the application open is a contributant to your problem...