This sounds like a similar problem to that reported in different guises in several threads here (see for example https://community.mcafee.com/message/203914#203914 a week ago or https://community.mcafee.com/thread/38280?start=0&tstart=0 with problems scanning files on a DVD drive but with otherwise similar symptoms - for some reason, although there are all these reports of similar problems with scanning hang-ups, McAfee don't seem to be linking them or doing much about them - don't understand why).
Certain files or file types cause scheduled scanning to slow to a snail's pace and lock up the computer while doing so. The scan doesn't actually stop but slows right down, typically with the drive accessing continuously but little CPU activity. If you waited long enough, you would probably find that the computer would eventually emerge at the end of the scan. I reckoned that in my own case, a full scan would take close to a week whereas, before the broken software update, it used to take less than an hour.
McAfee VirusScan whitelists some files once scanned and doesn't scan them again until new definitions are issued. This probably accounts for the erratic occurrence of the problem. Your problem files simply don't get scanned every time.
McAfee's solution to the problem seems to be to locate the files or folders on which the scan gets stuck and put them into a manual whitelist which will never get scanned again. I did this as a temporary workaround and it at least allows my scans to finish although still taking longer than before and behaving in an unusable way while a scan is in progress. You might wish to try this but, as far as I'm concerned, it is an unsatisfactory solution.
In my case, this has now been the situation for a few months and I'm not happy. McAfee may eventually come up with a fix to their scanner but don't hold your breath! I shall not be around to find out. I've just been waiting to see out my existing McAfee subscription and then I'm off to a different security provider. This time has now arrived.