There was a known issue that left the issues as "Running" even when they were completed. This is not exactly the same, but that was fixed some time ago and the newest release should have it fixed as well (11.20 SR3 12018).
As for the log files timestamp... Do you see any strange time (UTC) in the QMC that does not match with the server operating system time? Is the server running any NTP service that might create confussion? If you copy those files to another folder, does the original newer time still appears, or it does the new one?
The issue about leaving tasks as "running" was indeed fixed in an earlier release of version 11.0.
But I missed mentioning in my post that we're using version 11.20 SR2.
I'll add also that we have the publisher and using cluster server, thus a shared folder where documents/logs/etc. are stored.
Note that when I ran the task manually from QMC, its status remained as "Failed", not only after it was completed but also during the process, it didn't change to "Running" (I had to constantly check the log entry to make sure that the task was actually running).
Concerning the log entries timestamp, the main/cluster servers show the correct date/time but we had many tasks having log entries with dates in the future (like 2nd august 2013, while we were still on the 1st, or a date in september 2013, or even another in 2014 !).
When checking the folder DistributionService > 1 > Log, I didn't find them all in there but I removed anyways the ones with a future date, however in the QMC these future logs were still appearing.
I read later in another thread that log files are stored under folder ManagementService, not DistributionService.
So what I was thinking is that if I get to remove from this folder all the log files having a future date, maybe this will fix the task status in the QMC. Don't you think so ?
I'm probably going to client site in the morning so I'll try to proceed with the above step, and maybe attach some snapshots of the QMC to illustrate.
I'll also check whether they're running any NTP service as you suggested.
I'll appreciate if you have other suggestions to check, maybe based on the additional info above.