After much troubleshooting and getting Qlik support involved, the exact cause of this issue has been pinpointed, but not resolved. Here's what we believe is going on.
In our model, we build one large application, and then at distribution time, we loop and reduce to get separate applications for each of our customers. However, we use Section Access which is added to the large app. We thought that during the loop and reduce function that the Section Access would be reduced to only include users for the single customer app, but we learned that's not how Section Access works. What was actually happening was that all of the data EXCEPT Section Access was being reduced to just one customer; each individual app had the Section Access for ALL customers in it. Section Access does not reduce like everything else. So, QlikView was trying to keep track of SA for all customers in each application and as we added more and more customers, it was unable to do so.
QlikView said that the software was 'operating as designed', in other words, they never intended that SA would reduce along with the rest of the data. And, since we are the only ones currently seeing this 'issue', they are not inclined to do anything about it for the time being. Please note, I'm not bad-mouthing Qlik, just letting you know what they said, they were actually very helpful in troubleshooting this issue. So how did we fix it?
We looked at how we could reduce the number of UserIDs that were included in each application and found some efficiencies. We reduced the number of Users that were being brought into SA and our distribution failures went away. We realize this is a 'band-aid' fix, and we are looking at adding structure to our user base so that we can perhaps break our large apps into smaller groups prior to distribution which would further reduce the number of Users in the SA.