I guess you have checked this already and/or it will not be applicable to your scenario, but - we have experienced that here and there, never en masse as in your case. The reason here was always that the user's password had expired due to company_policy and had not been changed, so "physical" network_access to the directory where we store all our QV_apps was not available anymore.
What error does the end user sees when it starting to fail? Not what you see in the logs, but what error end-users sees in the process of opening the document. This is key because it could be, lack of CALs, Section Access or a true Qlik defect.
Now when you say " After about a week the failures reappeared." this still in SR5 or SR6? if still persist in SR5, it seems not to be a version problem, but something that changes, either in Qlikview and/or environment.