I’m going to put my two cents worth in.
I’ve been using Avast for some 4 years now and run a scheduled Full System Scan at 02:00 every day. This might sound excessive as others have pointed out but since I use laptops exclusively running a scan that reads all the data stored on your hard disk/s can give you forewarning of a disk that’s on its way out and allow you to get all your valuable data and software off before it goes legs up permanently. I do also do a full system backup every 2 weeks to an external drive but you can still save up to 2 weeks of work knowing you have a disk on the way out. It also minimizes downtime as it gives you time to get a replacement disk ready.
Anyway, back to the problems of the scans not running at the correct time. This has only been a problem for me since it was upgraded from the 2014 version to the 2015 versions and as far as I can tell it’s using UTC, GMT, Zulu, whatever you want to call it time and the log files state the UTC time and date not the local time and date.
I telephoned the call centre about it and as expected they told me to uninstall and then reinstall the software using a fresh download as Wi-Fi isn’t 100% reliable and the original update could have been corrupted. It’s pretty hard for a Wi-Fi link to corrupt a file when our in house network is all CAT5 or CAT6 cable running at 1000/100 Mb/s but the technical support person at the other end didn’t seem to understand that people do actually use extremely reliable, much faster and secure cable networks to connect to the internet.
Anyway I gave it a go just in case and as expected it didn’t fix the problem.
Having said all that, I never had any problems on the two machines I have used Avast on over the years until it upgraded from the 2014 version to the 2015 version, so for me at least it would appear to be some problem in the 2015 release.