The MMQAQC object listens to the document events like CloseDocument in ArcMap to display the message that QAQC is still processing. Have you tried fully releasing the MMQAQC object when you are done using it? I would recommend using something like the following, immediately after you are done with your QA process and have put the results in the list you are using.
how simple ;-).
Personally I like Marshal.ReleaseComObject(QaQc).
Not trying to add any confusion but one thread What's Up with ComReleaser? Is it really working? at Esri does suggest there's a lot among ArcGIS/ArcFM developers.
"In ArcObjects, singleton objects require instantiation through the Activator class and require explicit release via the ComReleaser class.", led me there.